## Souplet, Philippe

Compute Distance To:
 Author ID: souplet.philippe Published as: Souplet, Philippe; Souplet, Ph.
 Documents Indexed: 121 Publications since 1991, including 2 Books Co-Authors: 45 Co-Authors with 79 Joint Publications 1,089 Co-Co-Authors
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### Co-Authors

 42 single-authored 14 Quittner, Pavol 9 Weissler, Fred B. 5 Tayachi, Slim 4 Guo, Jong-Shenq 4 Mizoguchi, Noriko 4 Winkler, Michael 4 Zhang, Qi-Shuhuason 3 Fila, Marek 3 Laurençot, Philippe 3 Matos, Júlia 3 Porretta, Alessio 3 Sirakov, Boyan Slavchev 2 Attouchi, Amal 2 Ben-Artzi, Matania 2 Esteve, Carlos 2 Filippucci, Roberta 2 Martel, Yvan 2 Montaru, Alexandre 2 Phan Quoc Hung 2 Poláčik, Peter 2 Pucci, Patrizia 1 Ammar, Kaouther 1 Arrieta, José M. 1 Balabane, Mikhael 1 Bartier, Jean-Philippe 1 Bedjaoui, Nabil 1 Benachour, Said 1 Dickstein, Flávio 1 Dupaigne, Louis 1 Ghidouche, Hamid 1 Haraux, Alain 1 Jazar, Mustapha 1 Jleli, Mohamed Boussairi 1 Kavallaris, Nikos I. 1 Ling, Chia-Tung 1 Mahmoudi, Nejib 1 Manasevich, Raul F. 1 Phan, Quoc Hung 1 Rodríguez-Bernal, Aníbal 1 Rossi, Julio Daniel 1 Samet, Bessem 1 Schmitt, Didier 1 Tarzia, Domingo Alberto 1 Vazquez, Juan Luis 1 Yuxiang, Li
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### Serials

 6 Journal of Differential Equations 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 SIAM Journal on Mathematical Analysis 5 Discrete and Continuous Dynamical Systems 4 Proceedings of the American Mathematical Society 4 Comptes Rendus de l’Académie des Sciences. Série I 3 Communications in Mathematical Physics 3 Advances in Mathematics 3 Indiana University Mathematics Journal 3 Mathematische Annalen 3 Differential and Integral Equations 3 Communications in Partial Differential Equations 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 3 Nonlinear Analysis. Theory, Methods & Applications 2 Archive for Rational Mechanics and Analysis 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Analysis and Applications 2 Mathematical Methods in the Applied Sciences 2 Nonlinearity 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Colloquium Mathematicum 2 Duke Mathematical Journal 2 Journal of Functional Analysis 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Asymptotic Analysis 2 IMRN. International Mathematics Research Notices 2 Calculus of Variations and Partial Differential Equations 2 Advances in Differential Equations 2 Journal of Evolution Equations 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Birkhäuser Advanced Texts. Basler Lehrbücher 1 Houston Journal of Mathematics 1 Journal of Mathematical Biology 1 Mathematical Biosciences 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Bulletin of the London Mathematical Society 1 Journal of the Mathematical Society of Japan 1 Portugaliae Mathematica 1 Quarterly of Applied Mathematics 1 Transactions of the American Mathematical Society 1 European Journal of Applied Mathematics 1 Acta Mathematica Universitatis Comenianae. New Series 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Dynamics and Differential Equations 1 Electronic Journal of Differential Equations (EJDE) 1 NoDEA. Nonlinear Differential Equations and Applications 1 The Journal of Fourier Analysis and Applications 1 Interfaces and Free Boundaries 1 Journal of the European Mathematical Society (JEMS) 1 Portugaliae Mathematica. Nova Série 1 Advanced Nonlinear Studies 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S 1 SN Partial Differential Equations and Applications
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### Fields

 114 Partial differential equations (35-XX) 8 Ordinary differential equations (34-XX) 6 Biology and other natural sciences (92-XX) 4 Functional analysis (46-XX) 4 Operator theory (47-XX) 3 Integral equations (45-XX) 3 Mechanics of deformable solids (74-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Numerical analysis (65-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

113 Publications have been cited 2,830 times in 1,698 Documents Cited by Year
Superlinear parabolic problems. Blow-up, global existence and steady states. Zbl 1128.35003
Quittner, Pavol; Souplet, Philippe
2007
Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
2007
Blow-up in nonlocal reaction-diffusion equations. Zbl 0909.35073
Souplet, Philippe
1998
Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source. Zbl 0923.35077
Souplet, Philippe
1999
The proof of the Lane-Emden conjecture in four space dimensions. Zbl 1171.35035
Souplet, Philippe
2009
Nondegeneracy of blow-up points for the parabolic Keller-Segel system. Zbl 1302.35075
Mizoguchi, Noriko; Souplet, Philippe
2014
Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds. Zbl 1109.58025
Souplet, Philippe; Zhang, Qi S.
2006
Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
2007
Liouville-type theorems and bounds of solutions of Hardy-Hénon equations. Zbl 1233.35093
Phan Quoc Hung; Souplet, Philippe
2012
The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces. Zbl 1046.35046
Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B.
2002
Finite time blow-up for a nonlinear parabolic equation with a gradient term and applications. Zbl 0858.35067
Souplet, Philippe
1996
Optimal condition for non-simultaneous blow-up in a reaction-diffusion system. Zbl 1059.35049
Souplet, Philippe; Tayachi, Slim
2004
Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions. Zbl 1015.35016
Souplet, Philippe
2002
A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces. Zbl 1113.35062
Quittner, P.; Souplet, Ph.
2004
Superlinear parabolic problems. Blow-up, global existence and steady states. 2nd revised and updated edition. Zbl 1423.35004
Quittner, Pavol; Souplet, Philippe
2019
Self-similar subsolutions and blowup for nonlinear parabolic equations. Zbl 0892.35011
Souplet, Philippe; Weissler, Fred B.
1997
Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system. Zbl 1212.35219
Rossi, Julio D.; Souplet, Philippe
2005
Recent results and open problems on parabolic equations with gradient nonlinearities. Zbl 0982.35054
Souplet, Philippe
2001
Global solutions of inhomogeneous Hamilton-Jacobi equations. Zbl 1149.35050
Souplet, Philippe; Zhang, Qi S.
2006
Linear and nonlinear heat equations in $$L^q_\delta$$ spaces and universal bounds for global solutions. Zbl 0993.35023
Fila, Marek; Souplet, Philippe; Weissler, Fred B.
2001
Decay of global solutions, stability and blow up for a reaction-diffusion problem with free boundary. Zbl 0959.35087
Ghidouche, Hamid; Souplet, Philippe; Tarzia, Domingo
2001
Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103
Fila, Marek; Souplet, Philippe
2001
Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains. Zbl 1218.35052
Yuxiang, Li; Souplet, Philippe
2010
Symmetry of components for semilinear elliptic systems. Zbl 1255.35111
Quittner, Pavol; Souplet, Philippe
2012
The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046
Fila, Marek; Souplet, Philippe
2001
Uniform blow up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping. Zbl 1058.35121
Souplet, Philippe
2004
Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk. Zbl 1387.35354
Kavallaris, Nikos I.; Souplet, Philippe
2009
Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications. Zbl 1254.35077
Quittner, Pavol; Souplet, Philippe
2012
Critical blowup exponents for a system of reaction-diffusion equations with absorption. Zbl 0996.35029
Bedjaoui, Nabil; Souplet, Philippe
2002
Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations. Zbl 0892.35078
Souplet, Philippe
1998
Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state. Zbl 1029.35106
Souplet, Philippe; Weissler, Fred B.
2003
Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory. Zbl 1099.35049
Souplet, Philippe
2004
Global existence of solutions for a chemotaxis-type system arising in crime modelling. Zbl 1284.35445
Manásevich, Raúl; Phan Quoc Hung; Souplet, Philippe
2013
Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena. Zbl 1072.35098
Rodriguez-Bernal, Anibal; Arrieta, José M.; Souplet, Philippe
2004
Extinction and non-extinction for viscous Hamilton-Jacobi equations in $$\mathbb{R}^N$$. Zbl 1046.35053
Benachour, S.; Laurençot, Ph.; Schmitt, D.; Souplet, Ph.
2002
On the growth of mass for a viscous Hamilton-Jacobi equation. Zbl 1031.35054
Laurençot, Philippe; Souplet, Philippe
2003
Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term. Zbl 0990.35061
Souplet, Philippe; Tayachi, Slim; Weissler, Fred B.
1996
Poincaré’s inequality and global solutions of a nonlinear parabolic equation. Zbl 0924.35065
Souplet, Philippe; Weissler, Fred B.
1999
Single-point blow-up for a semilinear parabolic system. Zbl 1171.35059
Souplet, Philippe
2009
Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027
Quittner, Pavol; Souplet, Philippe; Winkler, Michael
2004
Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. Zbl 1116.35070
Souplet, Philippe; Vázquez, Juan Luis
2006
Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up. Zbl 1063.35087
Guo, Jong-Shenq; Souplet, Philippe
2005
Optimal regularity conditions for elliptic problems via $$L^p_\delta$$-spaces. Zbl 1130.35057
Souplet, Philippe
2005
Uniqueness and nonuniqueness results for the antiperiodic solutions of some second-order nonlinear evolution equations. Zbl 0855.34075
Souplet, Philippe
1996
Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations. Zbl 0926.35064
Souplet, Philippe
1999
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $${n\geq 3}$$. Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
2019
Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth. Zbl 07003366
Souplet, Philippe
2018
Transversality of stable and Nehari manifolds for a semilinear heat equation. Zbl 1233.35045
Dickstein, Flavio; Mizoguchi, Noriko; Souplet, Philippe; Weissler, Fred
2011
Admissible $$L_p$$ norms for local existence and for continuation in semilinear parabolic systems are not the same. Zbl 1006.35048
Quittner, Pavol; Souplet, Philippe
2001
Blowup rates for nonlinear heat equations with gradient terms and for parabolic inequalities. Zbl 0984.35077
Souplet, Philippe; Tayachi, Slim
2001
Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems. Zbl 1298.35060
Montaru, Alexandre; Sirakov, Boyan; Souplet, Philippe
2014
Universal blow-up rates for a semilinear heat equation and applications. Zbl 1028.35065
Matos, Júlia; Souplet, Philippe
2003
No touchdown at zero points of the permittivity profile for the MEMS problem. Zbl 1332.35160
Guo, Jong-Shenq; Souplet, Philippe
2015
Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations. Zbl 1007.35040
Souplet, Philippe
2002
On nonexistence and nonuniqueness of solutions of the Cauchy problem for a semilinear parabolic equation. (Sur la non-existence et la non-unicité des solutions du problème de Cauchy pour une équation parabolique semi-linéaire.) Zbl 0938.35068
Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B.
1999
Analysis of the loss of boundary conditions for the diffusive Hamilton-Jacobi equation. Zbl 1391.35078
Porretta, Alessio; Souplet, Philippe
2017
Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in $$\mathbb{R}^n$$. Zbl 1372.35157
Souplet, Philippe
2017
Improved conditions for single-point blow-up in reaction-diffusion systems. Zbl 1320.35097
Mahmoudi, Nejib; Souplet, Philippe; Tayachi, Slim
2015
Stability for semilinear parabolic equations with decaying potentials in $$\mathbb{R}^n$$ and dynamical approach to the existence of ground states. Zbl 1017.35033
Souplet, Philippe; Zhang, Qi S.
2002
Decay of heat semigroups in $$L^\infty$$ and applications to nonlinear parabolic problems in unbounded domains. Zbl 0954.35032
Souplet, Philippe
2000
The profile of boundary gradient blowup for the diffusive Hamilton-Jacobi equation. Zbl 1405.35097
Porretta, Alessio; Souplet, Philippe
2017
Nonexistence of global solutions to some differential inequalities of the second order and applications. Zbl 0843.34017
Souplet, Philippe
1995
Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Zbl 1195.35077
Ammar, Kaouther; Souplet, Philippe
2010
Parabolic Liouville-type theorems via their elliptic counterparts. Zbl 1306.35066
Quittner, Pavol; Souplet, Philippe
2011
Excluding blowup at zero points of the potential by means of Liouville-type theorems. Zbl 1394.35229
Guo, Jong-Shenq; Souplet, Philippe
2018
On the asymptotics of global solutions for a semilinear heat equation in unbounded domains. (Sur l’asymptotique des solutions globales pour une équation de la chaleur semi-linéaire dans des domaines non bornés.) Zbl 0860.35051
Souplet, Philippe
1996
Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation. Zbl 1437.35112
Porretta, Alessio; Souplet, Philippe
2020
Finite time blow up for a nonlinear heat equation. (Résultats d’explosion en temps fini pour une équation de la chaleur non linéaire.) Zbl 0843.35044
Souplet, Philippe
1995
Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079
Martel, Yvan; Souplet, Philippe
2000
Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices. Zbl 1263.35100
Souplet, Philippe
2012
Non-self-similar dead-core rate for the fast diffusion equation with strong absorption. Zbl 1194.35059
Guo, Jong-Shenq; Ling, Chia-Tung; Souplet, Philippe
2010
A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient. Zbl 1318.35018
Souplet, Philippe
2015
Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $$p$$-Laplacian diffusion. Zbl 1353.35070
Attouchi, Amal; Souplet, Philippe
2017
A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems. Zbl 1362.35063
Phan, Quoc Hung; Souplet, Philippe
2016
Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. Zbl 1383.35098
Souplet, Philippe; Tayachi, Slim
2016
Existence of exceptional growing-up solutions for a class of nonlinear second order ordinary differential equations. Zbl 0849.34024
Souplet, Philippe
1995
The influence of gradient perturbations on blow-up asymptotics in semilinear parabolic problems: a survey. Zbl 1094.35060
Souplet, Philippe
2005
Bounds of global solutions of parabolic problems with nonlinear boundary conditions. Zbl 1080.35039
Quittner, Pavol; Souplet, Philippe
2003
A survey on $$L^p_\delta$$ spaces and their applications to nonlinear elliptic and parabolic problems. Zbl 1080.35026
Souplet, Philippe
2004
An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source. Zbl 1172.35038
Souplet, Philippe
2009
Critical exponents, special large-time behavior and oscillatory blow-up in nonlinear ODE’s. Zbl 1015.34038
Souplet, Philippe
1998
Oscillatory blow-up in nonlinear second order ODE’s: The critical case. Zbl 1048.34074
Balabane, Mikhaël; Jazar, Mustapha; Souplet, Philippe
2003
A priori and universal estimates for global solutions of superlinear degenerate parabolic equations. Zbl 1072.35099
Souplet, Philippe
2002
A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton-Jacobi equations. Zbl 1436.35010
Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe
2020
Blow-up rate of solutions of parabolic problems with nonlinear boundary conditions. Zbl 1364.35175
Quittner, Pavol; Souplet, Philippe
2012
A note on diffusion-induced blow-up. Zbl 1145.35068
Souplet, Philippe
2007
Self-similar subsolutions and blow-up for nonlinear parabolic equations. Zbl 0893.35056
Souplet, Philippe; Weissler, Fred B.
1997
Étude des solutions globales de certaines équations différentielles ordinaires du second ordre non linéaires. (Study of the global solutions of certain nonlinear second order ordinary differential equations). Zbl 0738.34003
Souplet, Philippe
1991
A priori estimates of global solutions of superlinear parabolic problems without variational structure. Zbl 1029.35049
Quittner, Pavol; Souplet, Philippe
2003
An example of uniformly recurrent function which is not almost periodic. Zbl 1051.42008
Haraux, Alain; Souplet, Philippe
2004
Optimal condition for blow-up of the critical $$L^q$$ norm for the semilinear heat equation. Zbl 1420.35139
Mizoguchi, Noriko; Souplet, Philippe
2019
Global existence from single-component $$L_{p}$$ estimates in a semilinear reaction-diffusion system. Zbl 0993.35048
Quittner, Pavol; Souplet, Philippe
2002
Optimal growth rates for a viscous Hamilton-Jacobi equation. Zbl 1090.35036
Laurençot, Philippe; Souplet, Philippe
2005
The influence of space dimension on the large-time behavior in a reaction-diffusion system modeling diallelic selection. Zbl 1303.92086
Souplet, Philippe; Winkler, Michael
2011
Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities. Zbl 1439.35199
Jleli, Mohamed; Samet, Bessem; Souplet, Philippe
2020
A simplified approach to the refined blowup behavior for the nonlinear heat equation. Zbl 1411.35176
Souplet, Philippe
2019
Small time boundary estimates for solutions of the heat equation with non-compatible data. (Estimation optimales en temps petit et près de la frontière pour les solutions de l’équation de la chaleur avec données non compatibles.) Zbl 0990.35051
Martel, Yvan; Souplet, Philippe
1998
An optimal uniqueness condition for the antiperiodic solutions of parabolic evolution equations. (Une condition optimale d’unicité pour les solutions antipériodiques d’équations d’évolution paraboliques.) Zbl 0809.35036
Souplet, Philippe
1994
Gradient bounds for solutions of semilinear parabolic equations without Bernstein’s quadratic condition. Zbl 1073.35045
Bartier, Jean-Philippe; Souplet, Philippe
2004
Instantaneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations. Zbl 1052.35090
Matos, Júlia; Souplet, Philippe
2004
The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients. Zbl 1471.35138
Sirakov, Boyan; Souplet, Philippe
2021
Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation. Zbl 1437.35112
Porretta, Alessio; Souplet, Philippe
2020
A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton-Jacobi equations. Zbl 1436.35010
Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe
2020
Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities. Zbl 1439.35199
Jleli, Mohamed; Samet, Bessem; Souplet, Philippe
2020
A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient. Zbl 1440.35106
Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe
2020
Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations. Zbl 1448.35051
Attouchi, Amal; Souplet, Philippe
2020
Superlinear parabolic problems. Blow-up, global existence and steady states. 2nd revised and updated edition. Zbl 1423.35004
Quittner, Pavol; Souplet, Philippe
2019
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $${n\geq 3}$$. Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
2019
Optimal condition for blow-up of the critical $$L^q$$ norm for the semilinear heat equation. Zbl 1420.35139
Mizoguchi, Noriko; Souplet, Philippe
2019
A simplified approach to the refined blowup behavior for the nonlinear heat equation. Zbl 1411.35176
Souplet, Philippe
2019
No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem. Zbl 1444.35104
Esteve, Carlos; Souplet, Philippe
2019
Corrigendum to: “Nondegeneracy of blow-up points for the parabolic Keller-Segel system”. Zbl 1415.35062
Mizoguchi, N.; Souplet, Ph.
2019
Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth. Zbl 07003366
Souplet, Philippe
2018
Excluding blowup at zero points of the potential by means of Liouville-type theorems. Zbl 1394.35229
Guo, Jong-Shenq; Souplet, Philippe
2018
Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity. Zbl 1397.35127
Esteve, Carlos; Souplet, Philippe
2018
Analysis of the loss of boundary conditions for the diffusive Hamilton-Jacobi equation. Zbl 1391.35078
Porretta, Alessio; Souplet, Philippe
2017
Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in $$\mathbb{R}^n$$. Zbl 1372.35157
Souplet, Philippe
2017
The profile of boundary gradient blowup for the diffusive Hamilton-Jacobi equation. Zbl 1405.35097
Porretta, Alessio; Souplet, Philippe
2017
Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $$p$$-Laplacian diffusion. Zbl 1353.35070
Attouchi, Amal; Souplet, Philippe
2017
A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems. Zbl 1362.35063
Phan, Quoc Hung; Souplet, Philippe
2016
Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. Zbl 1383.35098
Souplet, Philippe; Tayachi, Slim
2016
No touchdown at zero points of the permittivity profile for the MEMS problem. Zbl 1332.35160
Guo, Jong-Shenq; Souplet, Philippe
2015
Improved conditions for single-point blow-up in reaction-diffusion systems. Zbl 1320.35097
Mahmoudi, Nejib; Souplet, Philippe; Tayachi, Slim
2015
A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient. Zbl 1318.35018
Souplet, Philippe
2015
Nondegeneracy of blow-up points for the parabolic Keller-Segel system. Zbl 1302.35075
Mizoguchi, Noriko; Souplet, Philippe
2014
Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems. Zbl 1298.35060
Montaru, Alexandre; Sirakov, Boyan; Souplet, Philippe
2014
Symmetry of components and Liouville theorems for noncooperative elliptic systems on the half-space. (Symétrie des composantes et théorèmes de Liouville pour des systèmes elliptiques non coopératifs dans le demi-espace.) Zbl 1300.35032
Montaru, Alexandre; Souplet, Philippe
2014
Global existence of solutions for a chemotaxis-type system arising in crime modelling. Zbl 1284.35445
Manásevich, Raúl; Phan Quoc Hung; Souplet, Philippe
2013
Liouville-type theorems and bounds of solutions of Hardy-Hénon equations. Zbl 1233.35093
Phan Quoc Hung; Souplet, Philippe
2012
Symmetry of components for semilinear elliptic systems. Zbl 1255.35111
Quittner, Pavol; Souplet, Philippe
2012
Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications. Zbl 1254.35077
Quittner, Pavol; Souplet, Philippe
2012
Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices. Zbl 1263.35100
Souplet, Philippe
2012
Blow-up rate of solutions of parabolic problems with nonlinear boundary conditions. Zbl 1364.35175
Quittner, Pavol; Souplet, Philippe
2012
Classification of large-time behaviors in a reaction-diffusion system modeling diallelic selection. Zbl 1319.92032
Souplet, Philippe; Winkler, Michael
2012
Transversality of stable and Nehari manifolds for a semilinear heat equation. Zbl 1233.35045
Dickstein, Flavio; Mizoguchi, Noriko; Souplet, Philippe; Weissler, Fred
2011
Parabolic Liouville-type theorems via their elliptic counterparts. Zbl 1306.35066
Quittner, Pavol; Souplet, Philippe
2011
The influence of space dimension on the large-time behavior in a reaction-diffusion system modeling diallelic selection. Zbl 1303.92086
Souplet, Philippe; Winkler, Michael
2011
Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains. Zbl 1218.35052
Yuxiang, Li; Souplet, Philippe
2010
Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Zbl 1195.35077
Ammar, Kaouther; Souplet, Philippe
2010
Non-self-similar dead-core rate for the fast diffusion equation with strong absorption. Zbl 1194.35059
Guo, Jong-Shenq; Ling, Chia-Tung; Souplet, Philippe
2010
The proof of the Lane-Emden conjecture in four space dimensions. Zbl 1171.35035
Souplet, Philippe
2009
Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk. Zbl 1387.35354
Kavallaris, Nikos I.; Souplet, Philippe
2009
Single-point blow-up for a semilinear parabolic system. Zbl 1171.35059
Souplet, Philippe
2009
An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source. Zbl 1172.35038
Souplet, Philippe
2009
Superlinear parabolic problems. Blow-up, global existence and steady states. Zbl 1128.35003
Quittner, Pavol; Souplet, Philippe
2007
Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
2007
Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
2007
A note on diffusion-induced blow-up. Zbl 1145.35068
Souplet, Philippe
2007
A remark on the large time behavior of solutions of viscous Hamilton-Jacobi equations. Zbl 1134.35019
Souplet, Philippe
2007
Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds. Zbl 1109.58025
Souplet, Philippe; Zhang, Qi S.
2006
Global solutions of inhomogeneous Hamilton-Jacobi equations. Zbl 1149.35050
Souplet, Philippe; Zhang, Qi S.
2006
Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. Zbl 1116.35070
Souplet, Philippe; Vázquez, Juan Luis
2006
Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system. Zbl 1212.35219
Rossi, Julio D.; Souplet, Philippe
2005
Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up. Zbl 1063.35087
Guo, Jong-Shenq; Souplet, Philippe
2005
Optimal regularity conditions for elliptic problems via $$L^p_\delta$$-spaces. Zbl 1130.35057
Souplet, Philippe
2005
The influence of gradient perturbations on blow-up asymptotics in semilinear parabolic problems: a survey. Zbl 1094.35060
Souplet, Philippe
2005
Optimal growth rates for a viscous Hamilton-Jacobi equation. Zbl 1090.35036
Laurençot, Philippe; Souplet, Philippe
2005
Optimal condition for non-simultaneous blow-up in a reaction-diffusion system. Zbl 1059.35049
Souplet, Philippe; Tayachi, Slim
2004
A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces. Zbl 1113.35062
Quittner, P.; Souplet, Ph.
2004
Uniform blow up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping. Zbl 1058.35121
Souplet, Philippe
2004
Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory. Zbl 1099.35049
Souplet, Philippe
2004
Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena. Zbl 1072.35098
Rodriguez-Bernal, Anibal; Arrieta, José M.; Souplet, Philippe
2004
Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027
Quittner, Pavol; Souplet, Philippe; Winkler, Michael
2004
A survey on $$L^p_\delta$$ spaces and their applications to nonlinear elliptic and parabolic problems. Zbl 1080.35026
Souplet, Philippe
2004
An example of uniformly recurrent function which is not almost periodic. Zbl 1051.42008
Haraux, Alain; Souplet, Philippe
2004
Gradient bounds for solutions of semilinear parabolic equations without Bernstein’s quadratic condition. Zbl 1073.35045
Bartier, Jean-Philippe; Souplet, Philippe
2004
Instantaneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations. Zbl 1052.35090
Matos, Júlia; Souplet, Philippe
2004
Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state. Zbl 1029.35106
Souplet, Philippe; Weissler, Fred B.
2003
On the growth of mass for a viscous Hamilton-Jacobi equation. Zbl 1031.35054
Laurençot, Philippe; Souplet, Philippe
2003
Universal blow-up rates for a semilinear heat equation and applications. Zbl 1028.35065
Matos, Júlia; Souplet, Philippe
2003
Bounds of global solutions of parabolic problems with nonlinear boundary conditions. Zbl 1080.35039
Quittner, Pavol; Souplet, Philippe
2003
Oscillatory blow-up in nonlinear second order ODE’s: The critical case. Zbl 1048.34074
Balabane, Mikhaël; Jazar, Mustapha; Souplet, Philippe
2003
A priori estimates of global solutions of superlinear parabolic problems without variational structure. Zbl 1029.35049
Quittner, Pavol; Souplet, Philippe
2003
The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces. Zbl 1046.35046
Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B.
2002
Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions. Zbl 1015.35016
Souplet, Philippe
2002
Critical blowup exponents for a system of reaction-diffusion equations with absorption. Zbl 0996.35029
Bedjaoui, Nabil; Souplet, Philippe
2002
Extinction and non-extinction for viscous Hamilton-Jacobi equations in $$\mathbb{R}^N$$. Zbl 1046.35053
Benachour, S.; Laurençot, Ph.; Schmitt, D.; Souplet, Ph.
2002
Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations. Zbl 1007.35040
Souplet, Philippe
2002
Stability for semilinear parabolic equations with decaying potentials in $$\mathbb{R}^n$$ and dynamical approach to the existence of ground states. Zbl 1017.35033
Souplet, Philippe; Zhang, Qi S.
2002
A priori and universal estimates for global solutions of superlinear degenerate parabolic equations. Zbl 1072.35099
Souplet, Philippe
2002
Global existence from single-component $$L_{p}$$ estimates in a semilinear reaction-diffusion system. Zbl 0993.35048
Quittner, Pavol; Souplet, Philippe
2002
Recent results and open problems on parabolic equations with gradient nonlinearities. Zbl 0982.35054
Souplet, Philippe
2001
Linear and nonlinear heat equations in $$L^q_\delta$$ spaces and universal bounds for global solutions. Zbl 0993.35023
Fila, Marek; Souplet, Philippe; Weissler, Fred B.
2001
Decay of global solutions, stability and blow up for a reaction-diffusion problem with free boundary. Zbl 0959.35087
Ghidouche, Hamid; Souplet, Philippe; Tarzia, Domingo
2001
Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103
Fila, Marek; Souplet, Philippe
2001
The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046
Fila, Marek; Souplet, Philippe
2001
Admissible $$L_p$$ norms for local existence and for continuation in semilinear parabolic systems are not the same. Zbl 1006.35048
Quittner, Pavol; Souplet, Philippe
2001
Blowup rates for nonlinear heat equations with gradient terms and for parabolic inequalities. Zbl 0984.35077
Souplet, Philippe; Tayachi, Slim
2001
Existence of ground states for semilinear elliptic equations with decaying mass: A parabolic approach. Zbl 0992.35029
Souplet, Philippe; Zhang, Qi S.
2001
Decay of heat semigroups in $$L^\infty$$ and applications to nonlinear parabolic problems in unbounded domains. Zbl 0954.35032
Souplet, Philippe
2000
Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079
Martel, Yvan; Souplet, Philippe
2000
Blow-up behavior in nonlocal vs. local heat equations. Zbl 0954.35091
Souplet, Philippe
2000
Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source. Zbl 0923.35077
Souplet, Philippe
1999
Poincaré’s inequality and global solutions of a nonlinear parabolic equation. Zbl 0924.35065
Souplet, Philippe; Weissler, Fred B.
1999
Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations. Zbl 0926.35064
Souplet, Philippe
1999
On nonexistence and nonuniqueness of solutions of the Cauchy problem for a semilinear parabolic equation. (Sur la non-existence et la non-unicité des solutions du problème de Cauchy pour une équation parabolique semi-linéaire.) Zbl 0938.35068
Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B.
1999
Sharp stability estimates for quasi-autonomous evolution equations of hyperbolic type. Zbl 1031.34059
Souplet, Philippe
1999
Blow-up in nonlocal reaction-diffusion equations. Zbl 0909.35073
Souplet, Philippe
1998
Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations. Zbl 0892.35078
Souplet, Philippe
1998
Critical exponents, special large-time behavior and oscillatory blow-up in nonlinear ODE’s. Zbl 1015.34038
Souplet, Philippe
1998
...and 13 more Documents
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### Cited by 1,578 Authors

 53 Souplet, Philippe 50 Winkler, Michael 47 Mu, Chunlai 31 Liu, Bingchen 31 Zheng, Sining 26 Li, Fengjie 22 Ishige, Kazuhiro 20 Wei, Juncheng 19 Fang, Zhongbo 18 Quittner, Pavol 17 Laurençot, Philippe 17 Zhang, Zhengce 16 Ding, Juntang 15 Fujishima, Yohei 15 Xiang, Zhaoyin 15 Xie, Chunhong 14 Lankeit, Johannes 14 Li, Yuxiang 14 Weissler, Fred B. 14 Zhou, Jun 13 Iagar, Razvan Gabriel 13 Kawakami, Tatsuki 13 Yanagida, Eiji 12 Quaas, Alexander 12 Wang, Liangchen 11 Fila, Marek 11 Guo, Zongming 11 Lin, Zhigui 11 Liu, Qilin 11 Mizoguchi, Noriko 11 Phan, Quoc Hung 11 Zheng, Pan 11 Zou, Wenming 10 Duong, Anh Tuan 10 Harrabi, Abdellaziz 10 Villavert, John 10 Wang, Mingxin 10 Wang, Wei 10 Wang, Yulan 10 Yang, Zuodong 10 Zaag, Hatem 9 Del Pino, Manuel A. 9 García-Melián, Jorge 9 Karch, Grzegorz 9 Poláčik, Peter 9 Tang, Bao Quoc 9 Tayachi, Slim 9 Wan, FangShu 8 Deng, Weibing 8 Du, Lili 8 Fellner, Klemens 8 Gao, Wenjie 8 Ghergu, Marius 8 Guo, Jong-Shenq 8 Lei, Yutian 8 Liu, Dengming 8 Musso, Monica 8 Parshad, Rana D. 8 Sierżȩga, Mikołaj 8 Song, Xianfa 8 Taliaferro, Steven D. 8 Weth, Tobias 8 Yin, Jingxue 7 Biler, Piotr 7 Chen, Caisheng 7 Chen, Youpeng 7 Chen, Yuqing 7 Harada, Junichi 7 Jin, Hai-Yang 7 Kong, Linghua 7 Liu, Baiyu 7 Loayza, Miguel 7 Nguyễn Thạc Dũng 7 Punzo, Fabio 7 Sánchez, Ariel 7 Stinner, Christian 7 Tao, Youshan 7 Wang, Xiaoliu 7 Yang, Hui 7 Yu, Xiaohui 6 Abdellaoui, Boumediene 6 Bidaut-Veron, Marie-Françoise 6 Dai, Wei 6 Ferreira, Raúl 6 Filippucci, Roberta 6 Fujie, Kentarou 6 Hu, Xuegang 6 Kirane, Mokhtar 6 Li, Congming 6 Li, Huiling 6 Morgan, Jeff J. 6 O’Regan, Donal 6 Rahal, Belgacem 6 Reichel, Wolfgang 6 Robinson, James Cooper 6 Rodríguez-Bernal, Aníbal 6 Shang, Haifeng 6 Takahashi, Jin 6 Vazquez, Juan Luis 6 Vernier-Piro, Stella ...and 1,478 more Authors
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### Cited in 230 Serials

 153 Journal of Differential Equations 147 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 138 Journal of Mathematical Analysis and Applications 47 Discrete and Continuous Dynamical Systems 45 Boundary Value Problems 38 Calculus of Variations and Partial Differential Equations 37 ZAMP. Zeitschrift für angewandte Mathematik und Physik 36 Journal of Functional Analysis 35 Applied Mathematics Letters 35 Nonlinear Analysis. Real World Applications 35 Communications on Pure and Applied Analysis 31 Computers & Mathematics with Applications 31 Journal de Mathématiques Pures et Appliquées. Neuvième Série 30 Applicable Analysis 27 Proceedings of the American Mathematical Society 26 Mathematische Annalen 26 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 25 Journal of Evolution Equations 23 Mathematical Methods in the Applied Sciences 23 Discrete and Continuous Dynamical Systems. Series B 21 Applied Mathematics and Computation 20 Advanced Nonlinear Studies 18 NoDEA. Nonlinear Differential Equations and Applications 14 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 14 Science China. Mathematics 13 Nonlinearity 13 Advances in Mathematics 13 Archiv der Mathematik 13 Communications in Partial Differential Equations 12 Journal of Mathematical Physics 12 SIAM Journal on Mathematical Analysis 12 Communications in Contemporary Mathematics 11 Transactions of the American Mathematical Society 11 Journal of Dynamics and Differential Equations 10 Journal of Inequalities and Applications 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Advances in Nonlinear Analysis 9 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Abstract and Applied Analysis 9 Acta Mathematica Sinica. English Series 9 Complex Variables and Elliptic Equations 9 SN Partial Differential Equations and Applications 8 Journal of Computational and Applied Mathematics 7 Journal d’Analyse Mathématique 7 Acta Applicandae Mathematicae 7 Mediterranean Journal of Mathematics 7 Discrete and Continuous Dynamical Systems. Series S 6 Communications in Mathematical Physics 6 Monatshefte für Mathematik 6 European Journal of Applied Mathematics 6 Applied Mathematics. Series B (English Edition) 6 Journal of Applied Mathematics and Computing 6 Journal of Elliptic and Parabolic Equations 5 Archive for Rational Mechanics and Analysis 5 Journal of Mathematical Biology 5 Quarterly of Applied Mathematics 5 Mathematical and Computer Modelling 5 The Journal of Geometric Analysis 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 SIAM Journal on Applied Mathematics 5 Stochastic Processes and their Applications 5 Potential Analysis 5 Milan Journal of Mathematics 5 Advances in Difference Equations 5 Journal of Function Spaces 5 AIMS Mathematics 4 Mathematical Notes 4 Duke Mathematical Journal 4 Journal of the Mathematical Society of Japan 4 Manuscripta Mathematica 4 Results in Mathematics 4 Tohoku Mathematical Journal. Second Series 4 Applied Mathematics and Mechanics. (English Edition) 4 Bulletin of the Iranian Mathematical Society 4 Japan Journal of Industrial and Applied Mathematics 4 Electronic Journal of Differential Equations (EJDE) 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Revista Matemática Complutense 4 Open Mathematics 4 Electronic Research Archive 3 Israel Journal of Mathematics 3 Rocky Mountain Journal of Mathematics 3 Chaos, Solitons and Fractals 3 International Journal of Mathematics and Mathematical Sciences 3 Journal of the Korean Mathematical Society 3 Mathematische Nachrichten 3 Pacific Journal of Mathematics 3 Chinese Annals of Mathematics. Series B 3 Physica D 3 Differential Geometry and its Applications 3 Bulletin des Sciences Mathématiques 3 Taiwanese Journal of Mathematics 3 Journal of Mathematical Fluid Mechanics 3 Communications in Nonlinear Science and Numerical Simulation 3 Annales Henri Poincaré 3 Differential Equations 3 Journal of Applied Mathematics 3 Journal of Fixed Point Theory and Applications 3 Frontiers of Mathematics in China 3 International Journal of Differential Equations ...and 130 more Serials
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### Cited in 37 Fields

 1,601 Partial differential equations (35-XX) 238 Biology and other natural sciences (92-XX) 74 Global analysis, analysis on manifolds (58-XX) 69 Ordinary differential equations (34-XX) 59 Integral equations (45-XX) 53 Differential geometry (53-XX) 42 Operator theory (47-XX) 42 Numerical analysis (65-XX) 38 Fluid mechanics (76-XX) 27 Functional analysis (46-XX) 25 Probability theory and stochastic processes (60-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 17 Mechanics of deformable solids (74-XX) 16 Real functions (26-XX) 15 Dynamical systems and ergodic theory (37-XX) 15 Systems theory; control (93-XX) 13 Classical thermodynamics, heat transfer (80-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Potential theory (31-XX) 11 Statistical mechanics, structure of matter (82-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 5 Difference and functional equations (39-XX) 5 Optics, electromagnetic theory (78-XX) 4 Functions of a complex variable (30-XX) 3 Mechanics of particles and systems (70-XX) 3 Quantum theory (81-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX)