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Souplet, Philippe

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 Author ID: souplet.philippe Published as: Souplet, Ph.; Souplet, Philippe
 Documents Indexed: 116 Publications since 1991, including 2 Books
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Co-Authors

 40 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 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 Porretta, Alessio 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 Ghidouche, Hamid 1 Haraux, Alain 1 Jazar, Mustapha 1 Jleli, Mohamed 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 Sirakov, Boyan Slavchev 1 Tarzia, Domingo Alberto 1 Vazquez, Juan Luis 1 Yuxiang, Li
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Serials

 6 Journal of Differential Equations 5 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 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 Advances in Mathematics 2 Duke Mathematical Journal 2 Journal of Functional Analysis 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Asymptotic Analysis 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 Colloquium Mathematicum 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 IMRN. International Mathematics Research Notices 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
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Fields

 109 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

108 Publications have been cited 2,479 times in 1,467 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
Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source. Zbl 0923.35077
Souplet, Philippe
1999
Blow-up in nonlocal reaction-diffusion equations. Zbl 0909.35073
Souplet, Philippe
1998
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
Finite time blow-up for a nonlinear parabolic equation with a gradient term and applications. Zbl 0858.35067
Souplet, Philippe
1996
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
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
Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions. Zbl 1015.35016
Souplet, Philippe
2002
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
Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103
Fila, Marek; Souplet, Philippe
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
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
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
Uniform blow up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping. Zbl 1058.35121
Souplet, Philippe
2004
The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046
Fila, Marek; Souplet, Philippe
2001
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
Poincaré’s inequality and global solutions of a nonlinear parabolic equation. Zbl 0924.35065
Souplet, Philippe; Weissler, Fred B.
1999
Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations. Zbl 0892.35078
Souplet, Philippe
1998
Global existence of solutions for a chemotaxis-type system arising in crime modelling. Zbl 1284.35445
Manásevich, Raúl; Phan Quoc Hung; Souplet, Philippe
2013
Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory. Zbl 1099.35049
Souplet, Philippe
2004
Critical blowup exponents for a system of reaction-diffusion equations with absorption. Zbl 0996.35029
Bedjaoui, Nabil; Souplet, Philippe
2002
Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications. Zbl 1254.35077
Quittner, Pavol; Souplet, Philippe
2012
Optimal regularity conditions for elliptic problems via $$L^p_\delta$$-spaces. Zbl 1130.35057
Souplet, Philippe
2005
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
On the growth of mass for a viscous Hamilton-Jacobi equation. Zbl 1031.35054
Laurençot, Philippe; Souplet, Philippe
2003
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
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
Superlinear parabolic problems. Blow-up, global existence and steady states. 2nd revised and updated edition. Zbl 1423.35004
Quittner, Pavol; Souplet, Philippe
2019
Single-point blow-up for a semilinear parabolic system. Zbl 1171.35059
Souplet, Philippe
2009
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
Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027
Quittner, Pavol; Souplet, Philippe; Winkler, Michael
2004
Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations. Zbl 0926.35064
Souplet, Philippe
1999
Uniqueness and nonuniqueness results for the antiperiodic solutions of some second-order nonlinear evolution equations. Zbl 0855.34075
Souplet, Philippe
1996
Transversality of stable and Nehari manifolds for a semilinear heat equation. Zbl 1233.35045
Dickstein, Flavio; Mizoguchi, Noriko; Souplet, Philippe; Weissler, Fred
2011
Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems. Zbl 1298.35060
Montaru, Alexandre; Sirakov, Boyan; Souplet, Philippe
2014
Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations. Zbl 1007.35040
Souplet, Philippe
2002
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
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $${n\geq 3}$$. Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
2019
Universal blow-up rates for a semilinear heat equation and applications. Zbl 1028.35065
Matos, Júlia; Souplet, Philippe
2003
Decay of heat semigroups in $$L^\infty$$ and applications to nonlinear parabolic problems in unbounded domains. Zbl 0954.35032
Souplet, Philippe
2000
On nonexistence and nonuniqueness of solutions of the Cauchy problem for a semilinear parabolic equation. Zbl 0938.35068
Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B.
1999
Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth. Zbl 07003366
Souplet, Philippe
2018
Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in $$\mathbb{R}^n$$. Zbl 1372.35157
Souplet, Philippe
2017
No touchdown at zero points of the permittivity profile for the MEMS problem. Zbl 1332.35160
Guo, Jong-Shenq; Souplet, Philippe
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
Nonexistence of global solutions to some differential inequalities of the second order and applications. Zbl 0843.34017
Souplet, Philippe
1995
Improved conditions for single-point blow-up in reaction-diffusion systems. Zbl 1320.35097
Mahmoudi, Nejib; Souplet, Philippe; Tayachi, Slim
2015
Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Zbl 1195.35077
Ammar, Kaouther; Souplet, Philippe
2010
The profile of boundary gradient blowup for the diffusive Hamilton-Jacobi equation. Zbl 1405.35097
Porretta, Alessio; Souplet, Philippe
2017
On the asymptotics of global solutions for a semilinear heat equation in unbounded domains. Zbl 0860.35051
Souplet, Philippe
1996
A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient. Zbl 1318.35018
Souplet, Philippe
2015
Parabolic Liouville-type theorems via their elliptic counterparts. Zbl 1306.35066
Quittner, Pavol; Souplet, Philippe
2011
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
Finite time blow up for a nonlinear heat equation. Zbl 0843.35044
Souplet, Philippe
1995
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
Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices. Zbl 1263.35100
Souplet, Philippe
2012
The influence of gradient perturbations on blow-up asymptotics in semilinear parabolic problems: a survey. Zbl 1094.35060
Souplet, Philippe
2005
A survey on $$L^p_\delta$$ spaces and their applications to nonlinear elliptic and parabolic problems. Zbl 1080.35026
Souplet, Philippe
2004
Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079
Martel, Yvan; Souplet, Philippe
2000
Existence of exceptional growing-up solutions for a class of nonlinear second order ordinary differential equations. Zbl 0849.34024
Souplet, Philippe
1995
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
Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. Zbl 1383.35098
Souplet, Philippe; Tayachi, Slim
2016
Blow-up rate of solutions of parabolic problems with nonlinear boundary conditions. Zbl 1364.35175
Quittner, Pavol; Souplet, Philippe
2012
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 and universal estimates for global solutions of superlinear degenerate parabolic equations. Zbl 1072.35099
Souplet, Philippe
2002
Critical exponents, special large-time behavior and oscillatory blow-up in nonlinear ODE’s. Zbl 1015.34038
Souplet, Philippe
1998
Excluding blowup at zero points of the potential by means of Liouville-type theorems. Zbl 1394.35229
Guo, Jong-Shenq; Souplet, Philippe
2018
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
An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source. Zbl 1172.35038
Souplet, Philippe
2009
A note on diffusion-induced blow-up. Zbl 1145.35068
Souplet, Philippe
2007
Optimal growth rates for a viscous Hamilton-Jacobi equation. Zbl 1090.35036
Laurençot, Philippe; Souplet, Philippe
2005
A priori estimates of global solutions of superlinear parabolic problems without variational structure. Zbl 1029.35049
Quittner, Pavol; Souplet, Philippe
2003
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 Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems. Zbl 1362.35063
Phan, Quoc Hung; Souplet, Philippe
2016
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
Corrigendum to: “Nondegeneracy of blow-up points for the parabolic Keller-Segel system”. Zbl 1415.35062
Mizoguchi, N.; Souplet, Ph.
2019
A simplified approach to the refined blowup behavior for the nonlinear heat equation. Zbl 1411.35176
Souplet, Philippe
2019
Symmetry of components and Liouville theorems for noncooperative elliptic systems on the half-space. Zbl 1300.35032
Montaru, Alexandre; Souplet, Philippe
2014
Gradient bounds for solutions of semilinear parabolic equations without Bernstein’s quadratic condition. Zbl 1073.35045
Bartier, Jean-Philippe; Souplet, Philippe
2004
Global existence from single-component $$L_{p}$$ estimates in a semilinear reaction-diffusion system. Zbl 0993.35048
Quittner, Pavol; Souplet, Philippe
2002
Small time boundary estimates for solutions of the heat equation with non-compatible data. Zbl 0990.35051
Martel, Yvan; Souplet, Philippe
1998
An optimal uniqueness condition for the antiperiodic solutions of parabolic evolution equations. Zbl 0809.35036
Souplet, Philippe
1994
Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities. Zbl 1439.35199
Jleli, Mohamed; Samet, Bessem; Souplet, Philippe
2020
No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem. Zbl 1444.35104
Esteve, Carlos; Souplet, Philippe
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
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
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
Corrigendum to: “Nondegeneracy of blow-up points for the parabolic Keller-Segel system”. Zbl 1415.35062
Mizoguchi, N.; Souplet, Ph.
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
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 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
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
Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. Zbl 1383.35098
Souplet, Philippe; Tayachi, Slim
2016
A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems. Zbl 1362.35063
Phan, Quoc Hung; Souplet, Philippe
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. 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
Optimal regularity conditions for elliptic problems via $$L^p_\delta$$-spaces. Zbl 1130.35057
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
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
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
An example of uniformly recurrent function which is not almost periodic. Zbl 1051.42008
Haraux, Alain; 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
Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103
Fila, Marek; Souplet, Philippe
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
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. 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
Small time boundary estimates for solutions of the heat equation with non-compatible data. Zbl 0990.35051
Martel, Yvan; Souplet, Philippe
1998
Some results on blow-up for nonlocal reaction-diffusion equations. Zbl 0919.35058
Souplet, Philippe
1998
Self-similar subsolutions and blowup for nonlinear parabolic equations. Zbl 0892.35011
Souplet, Philippe; Weissler, Fred B.
1997
Self-similar subsolutions and blow-up for nonlinear parabolic equations. Zbl 0893.35056
Souplet, Philippe; Weissler, Fred B.
1997
Finite time blow-up for a nonlinear parabolic equation with a gradient term and applications. Zbl 0858.35067
Souplet, Philippe
1996
...and 8 more Documents
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Cited by 1,458 Authors

 50 Souplet, Philippe 45 Mu, Chunlai 43 Winkler, Michael 30 Liu, Bingchen 30 Zheng, Sining 25 Li, Fengjie 19 Ishige, Kazuhiro 18 Wei, Juncheng 16 Laurençot, Philippe 16 Li, Yuxiang 15 Fang, Zhongbo 15 Quittner, Pavol 15 Xie, Chunhong 15 Zhang, Zhengce 14 Weissler, Fred B. 14 Zhou, Jun 13 Yanagida, Eiji 12 Ding, Juntang 11 Fila, Marek 11 Fujishima, Yohei 11 Kawakami, Tatsuki 11 Lankeit, Johannes 11 Lin, Zhigui 11 Liu, Qilin 11 Mizoguchi, Noriko 11 Phan, Quoc Hung 11 Quaas, Alexander 11 Xiang, Zhaoyin 11 Zheng, Pan 10 García-Melián, Jorge 10 Guo, Zongming 10 Iagar, Razvan Gabriel 10 Wang, Mingxin 10 Zou, Wenming 9 Karch, Grzegorz 9 Ma, Li 9 Poláčik, Peter 9 Song, Xianfa 9 Tayachi, Slim 9 Villavert, John 9 Wang, Liangchen 9 Wang, Wei 9 Zaag, Hatem 8 Del Pino, Manuel A. 8 Deng, Weibing 8 Du, Lili 8 Duong, Anh Tuan 8 Fellner, Klemens 8 Gao, Wenjie 8 Guo, Jong-Shenq 8 Harrabi, Abdellaziz 8 Lei, Yutian 8 Stinner, Christian 8 Tang, Bao Quoc 8 Wan, FangShu 8 Wang, Yulan 8 Weth, Tobias 8 Yang, Zuodong 7 Biler, Piotr 7 Chen, Youpeng 7 Chen, Yuqing 7 Harada, Junichi 7 Kong, Linghua 7 Liu, Baiyu 7 Musso, Monica 7 Parshad, Rana D. 7 Sierżȩga, Mikołaj 7 Taliaferro, Steven D. 7 Wang, Xiaoliu 7 Yu, Xiaohui 6 Chen, Caisheng 6 Ferreira, Raúl 6 Fujie, Kentarou 6 Hu, Xuegang 6 Li, Congming 6 Li, Huiling 6 Liu, Dengming 6 Loayza, Miguel 6 Reichel, Wolfgang 6 Robinson, James Cooper 6 Rodríguez-Bernal, Aníbal 6 Shang, Haifeng 6 Tao, Youshan 6 Vernier-Piro, Stella 6 Yang, Hui 6 Yin, Jingxue 6 Yokota, Tomomi 6 Zhang, Qingshan 5 Abdellaoui, Boumediene 5 Bao, Jiguang 5 Bidaut-Veron, Marie-Françoise 5 Brunner, Hermann 5 Cazenave, Thierry 5 Choi, Woocheol 5 Dai, Qiuyi 5 de Pablo, Arturo 5 Dickstein, Flávio 5 Dupaigne, Louis 5 Escher, Joachim 5 Ferreira, Lucas Catão de Freitas ...and 1,358 more Authors
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Cited in 201 Serials

 140 Journal of Differential Equations 140 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 128 Journal of Mathematical Analysis and Applications 44 Discrete and Continuous Dynamical Systems 39 Boundary Value Problems 35 Applied Mathematics Letters 33 Journal of Functional Analysis 32 ZAMP. Zeitschrift für angewandte Mathematik und Physik 32 Calculus of Variations and Partial Differential Equations 32 Nonlinear Analysis. Real World Applications 31 Computers & Mathematics with Applications 28 Applicable Analysis 26 Journal de Mathématiques Pures et Appliquées. Neuvième Série 25 Proceedings of the American Mathematical Society 24 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 23 Mathematical Methods in the Applied Sciences 23 Mathematische Annalen 23 Communications on Pure and Applied Analysis 19 Applied Mathematics and Computation 18 Discrete and Continuous Dynamical Systems. Series B 17 Journal of Evolution Equations 16 NoDEA. Nonlinear Differential Equations and Applications 16 Advanced Nonlinear Studies 13 Science China. Mathematics 12 Journal of Mathematical Physics 12 Communications in Partial Differential Equations 12 Communications in Contemporary Mathematics 11 Advances in Mathematics 10 Nonlinearity 10 Archiv der Mathematik 10 Transactions of the American Mathematical Society 10 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 10 Journal of Dynamics and Differential Equations 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 SIAM Journal on Mathematical Analysis 9 Abstract and Applied Analysis 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Journal of Computational and Applied Mathematics 8 Advances in Nonlinear Analysis 7 Journal d’Analyse Mathématique 7 Journal of Inequalities and Applications 7 Acta Mathematica Sinica. English Series 6 Communications in Mathematical Physics 6 Monatshefte für Mathematik 6 Acta Applicandae Mathematicae 6 European Journal of Applied Mathematics 6 Applied Mathematics. Series B (English Edition) 6 Journal of Applied Mathematics and Computing 6 Complex Variables and Elliptic Equations 6 Discrete and Continuous Dynamical Systems. Series S 5 Archive for Rational Mechanics and Analysis 5 Quarterly of Applied Mathematics 5 Mathematical and Computer Modelling 5 Stochastic Processes and their Applications 5 Potential Analysis 5 Milan Journal of Mathematics 5 Journal of Elliptic and Parabolic Equations 4 Journal of Mathematical Biology 4 Mathematical Notes 4 Manuscripta Mathematica 4 Tohoku Mathematical Journal. Second Series 4 Applied Mathematics and Mechanics. (English Edition) 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Electronic Journal of Differential Equations (EJDE) 4 Advances in Difference Equations 4 Journal of Function Spaces 3 Israel Journal of Mathematics 3 Rocky Mountain Journal of Mathematics 3 International Journal of Mathematics and Mathematical Sciences 3 Journal of the Korean Mathematical Society 3 Mathematische Nachrichten 3 Pacific Journal of Mathematics 3 Results in Mathematics 3 Japan Journal of Industrial and Applied Mathematics 3 Differential Geometry and its Applications 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Revista Matemática Complutense 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 Mediterranean Journal of Mathematics 3 Frontiers of Mathematics in China 3 International Journal of Differential Equations 3 Journal of Pseudo-Differential Operators and Applications 3 Analysis and Mathematical Physics 3 SN Partial Differential Equations and Applications 2 Journal of Engineering Mathematics 2 Mathematical Biosciences 2 Acta Mathematica 2 Czechoslovak Mathematical Journal 2 Geometriae Dedicata 2 Glasgow Mathematical Journal 2 Mathematische Zeitschrift 2 Zeitschrift für Analysis und ihre Anwendungen 2 Chinese Annals of Mathematics. Series B 2 Bulletin of the Iranian Mathematical Society 2 Physica D 2 Acta Mathematicae Applicatae Sinica. English Series ...and 101 more Serials
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Cited in 36 Fields

 1,385 Partial differential equations (35-XX) 183 Biology and other natural sciences (92-XX) 69 Ordinary differential equations (34-XX) 59 Global analysis, analysis on manifolds (58-XX) 54 Integral equations (45-XX) 38 Differential geometry (53-XX) 37 Operator theory (47-XX) 36 Numerical analysis (65-XX) 31 Fluid mechanics (76-XX) 22 Functional analysis (46-XX) 20 Probability theory and stochastic processes (60-XX) 15 Dynamical systems and ergodic theory (37-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Mechanics of deformable solids (74-XX) 13 Classical thermodynamics, heat transfer (80-XX) 13 Systems theory; control (93-XX) 12 Real functions (26-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Potential theory (31-XX) 9 Statistical mechanics, structure of matter (82-XX) 4 Difference and functional equations (39-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Mechanics of particles and systems (70-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Measure and integration (28-XX) 2 Abstract harmonic analysis (43-XX) 2 Quantum theory (81-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX)