Edit Profile (opens in new tab) Souplet, Philippe Co-Author Distance Author ID: souplet.philippe Published as: Souplet, Philippe; Souplet, Ph. Homepage: https://www.math.univ-paris13.fr/~souplet/indexEngl.html External Links: MGP · ORCID · Wikidata · ResearchGate · dblp · IdRef · theses.fr Documents Indexed: 133 Publications since 1991, including 2 Books and 9 Additional arXiv Preprints Co-Authors: 50 Co-Authors with 90 Joint Publications 1,342 Co-Co-Authors all top 5 Co-Authors 43 single-authored 16 Quittner, Pavol 9 Weissler, Fred B. 6 Mizoguchi, Noriko 5 Sirakov, Boyan Slavchev 5 Tayachi, Slim 4 Guo, Jong-Shenq 4 Winkler, Michael 4 Zhang, Qi-Shuhuason 3 Fila, Marek 3 Laurençot, Philippe 3 Matos, Júlia 3 Porretta, Alessio 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 Chabi, Loth Damagui 1 Dickstein, Flávio 1 Domínguez-de-Tena, Joaquín 1 Dupaigne, Louis 1 Ghidouche, Hamid 1 Haraux, Alain 1 Jazar, Mustapha 1 Jleli, Mohamed Boussairi 1 Kavallaris, Nikos Ioannis 1 Li, Yimei 1 Ling, Chia-Tung 1 Mahmoudi, Nejib 1 Manasevich, Raul F. 1 Meunier, Nicolas 1 Milišić, Vuk 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 all top 5 Serials 6 Journal of Differential Equations 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Discrete and Continuous Dynamical Systems 5 SIAM Journal on Mathematical Analysis 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 Asymptotic Analysis 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 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 The Journal of Geometric Analysis 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 all top 5 Fields 121 Partial differential equations (35-XX) 8 Ordinary differential equations (34-XX) 6 Biology and other natural sciences (92-XX) 4 Integral equations (45-XX) 4 Functional analysis (46-XX) 4 Operator theory (47-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 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 117 Publications have been cited 3,807 times in 2,323 Documents Cited by ▼ Year ▼ Superlinear parabolic problems. Blow-up, global existence and steady states. Zbl 1128.35003 Quittner, Pavol; Souplet, Philippe 689 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 254 2007 Nondegeneracy of blow-up points for the parabolic Keller-Segel system. Zbl 1302.35075 Mizoguchi, Noriko; Souplet, Philippe 219 2014 Blow-up in nonlocal reaction-diffusion equations. Zbl 0909.35073 Souplet, Philippe 172 1998 The proof of the Lane-Emden conjecture in four space dimensions. Zbl 1171.35035 Souplet, Philippe 169 2009 Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source. Zbl 0923.35077 Souplet, Philippe 160 1999 Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds. Zbl 1109.58025 Souplet, Philippe; Zhang, Qi S. 141 2006 Superlinear parabolic problems. Blow-up, global existence and steady states. 2nd revised and updated edition. Zbl 1423.35004 Quittner, Pavol; Souplet, Philippe 139 2019 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051 Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 91 2007 Liouville-type theorems and bounds of solutions of Hardy-Hénon equations. Zbl 1233.35093 Phan Quoc Hung; Souplet, Philippe 83 2012 The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces. Zbl 1046.35046 Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B. 67 2002 Finite time blow-up for a nonlinear parabolic equation with a gradient term and applications. Zbl 0858.35067 Souplet, Philippe 60 1996 A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces. Zbl 1113.35062 Quittner, P.; Souplet, Ph. 49 2004 Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions. Zbl 1015.35016 Souplet, Philippe 48 2002 Optimal condition for non-simultaneous blow-up in a reaction-diffusion system. Zbl 1059.35049 Souplet, Philippe; Tayachi, Slim 48 2004 Global solutions of inhomogeneous Hamilton-Jacobi equations. Zbl 1149.35050 Souplet, Philippe; Zhang, Qi S. 47 2006 Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system. Zbl 1212.35219 Rossi, Julio D.; Souplet, Philippe 43 2005 Self-similar subsolutions and blowup for nonlinear parabolic equations. Zbl 0892.35011 Souplet, Philippe; Weissler, Fred B. 42 1997 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140 Souplet, Philippe; Winkler, Michael 42 2019 Recent results and open problems on parabolic equations with gradient nonlinearities. Zbl 0982.35054 Souplet, Philippe 40 2001 Symmetry of components for semilinear elliptic systems. Zbl 1255.35111 Quittner, Pavol; Souplet, Philippe 35 2012 Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103 Fila, Marek; Souplet, Philippe 34 2001 Global existence of solutions for a chemotaxis-type system arising in crime modelling. Zbl 1284.35445 Manásevich, Raúl; Phan Quoc Hung; Souplet, Philippe 32 2013 Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains. Zbl 1218.35052 Yuxiang, Li; Souplet, Philippe 32 2010 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. 31 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 30 2001 Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications. Zbl 1254.35077 Quittner, Pavol; Souplet, Philippe 29 2012 The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046 Fila, Marek; Souplet, Philippe 28 2001 Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena. Zbl 1072.35098 Rodriguez-Bernal, Anibal; Arrieta, José M.; Souplet, Philippe 26 2004 Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth. Zbl 1516.35235 Souplet, Philippe 26 2018 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 26 2009 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. 24 2003 Uniform blow up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping. Zbl 1058.35121 Souplet, Philippe 23 2004 Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. Zbl 1116.35070 Souplet, Philippe; Vázquez, Juan Luis 23 2006 Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory. Zbl 1099.35049 Souplet, Philippe 22 2004 Optimal regularity conditions for elliptic problems via \(L^p_\delta\)-spaces. Zbl 1130.35057 Souplet, Philippe 21 2005 Single-point blow-up for a semilinear parabolic system. Zbl 1171.35059 Souplet, Philippe 21 2009 Extinction and non-extinction for viscous Hamilton-Jacobi equations in \(\mathbb{R}^N\). Zbl 1046.35053 Benachour, S.; Laurençot, Ph.; Schmitt, D.; Souplet, Ph. 20 2002 Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in \(\mathbb{R}^n\). Zbl 1372.35157 Souplet, Philippe 19 2017 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. 19 1996 Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations. Zbl 0892.35078 Souplet, Philippe 19 1998 On the growth of mass for a viscous Hamilton-Jacobi equation. Zbl 1031.35054 Laurençot, Philippe; Souplet, Philippe 19 2003 Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027 Quittner, Pavol; Souplet, Philippe; Winkler, Michael 19 2004 Critical blowup exponents for a system of reaction-diffusion equations with absorption. Zbl 0996.35029 Bedjaoui, Nabil; Souplet, Philippe 19 2002 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 18 2005 Poincaré’s inequality and global solutions of a nonlinear parabolic equation. Zbl 0924.35065 Souplet, Philippe; Weissler, Fred B. 18 1999 Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations. Zbl 0926.35064 Souplet, Philippe 17 1999 Analysis of the loss of boundary conditions for the diffusive Hamilton-Jacobi equation. Zbl 1391.35078 Porretta, Alessio; Souplet, Philippe 17 2017 Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems. Zbl 1298.35060 Montaru, Alexandre; Sirakov, Boyan; Souplet, Philippe 17 2014 Uniqueness and nonuniqueness results for the antiperiodic solutions of some second-order nonlinear evolution equations. Zbl 0855.34075 Souplet, Philippe 16 1996 Transversality of stable and Nehari manifolds for a semilinear heat equation. Zbl 1233.35045 Dickstein, Flavio; Mizoguchi, Noriko; Souplet, Philippe; Weissler, Fred 16 2011 Universal blow-up rates for a semilinear heat equation and applications. Zbl 1028.35065 Matos, Júlia; Souplet, Philippe 16 2003 No touchdown at zero points of the permittivity profile for the MEMS problem. Zbl 1332.35160 Guo, Jong-Shenq; Souplet, Philippe 16 2015 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 16 2001 The profile of boundary gradient blowup for the diffusive Hamilton-Jacobi equation. Zbl 1405.35097 Porretta, Alessio; Souplet, Philippe 16 2017 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 16 2020 Improved conditions for single-point blow-up in reaction-diffusion systems. Zbl 1320.35097 Mahmoudi, Nejib; Souplet, Philippe; Tayachi, Slim 15 2015 Blowup rates for nonlinear heat equations with gradient terms and for parabolic inequalities. Zbl 0984.35077 Souplet, Philippe; Tayachi, Slim 15 2001 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. 15 2002 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 14 2020 Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations. Zbl 1007.35040 Souplet, Philippe 13 2002 Excluding blowup at zero points of the potential by means of Liouville-type theorems. Zbl 1394.35229 Guo, Jong-Shenq; Souplet, Philippe 13 2018 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. 12 1999 Decay of heat semigroups in \(L^\infty\) and applications to nonlinear parabolic problems in unbounded domains. Zbl 0954.35032 Souplet, Philippe 12 2000 Optimal condition for blow-up of the critical \(L^q\) norm for the semilinear heat equation. Zbl 1420.35139 Mizoguchi, Noriko; Souplet, Philippe 11 2019 A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems. Zbl 1362.35063 Phan, Quoc Hung; Souplet, Philippe 11 2016 Nonexistence of global solutions to some differential inequalities of the second order and applications. Zbl 0843.34017 Souplet, Philippe 11 1995 Parabolic Liouville-type theorems via their elliptic counterparts. Zbl 1306.35066 Quittner, Pavol; Souplet, Philippe 11 2011 Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Zbl 1195.35077 Ammar, Kaouther; Souplet, Philippe 11 2010 An example of uniformly recurrent function which is not almost periodic. Zbl 1051.42008 Haraux, Alain; Souplet, Philippe 10 2004 A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient. Zbl 1440.35106 Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe 10 2020 An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source. Zbl 1172.35038 Souplet, Philippe 9 2009 The influence of gradient perturbations on blow-up asymptotics in semilinear parabolic problems: a survey. Zbl 1094.35060 Souplet, Philippe 9 2005 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 9 2010 A Liouville-type theorem for the Lane-Emden equation in a half-space. Zbl 1491.35089 Dupaigne, Louis; Sirakov, Boyan; Souplet, Philippe 8 2022 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 8 1996 A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient. Zbl 1318.35018 Souplet, Philippe 8 2015 Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079 Martel, Yvan; Souplet, Philippe 8 2000 Bounds of global solutions of parabolic problems with nonlinear boundary conditions. Zbl 1080.35039 Quittner, Pavol; Souplet, Philippe 8 2003 Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices. Zbl 1263.35100 Souplet, Philippe 8 2012 Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. Zbl 1383.35098 Souplet, Philippe; Tayachi, Slim 8 2016 Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities. Zbl 1439.35199 Jleli, Mohamed; Samet, Bessem; Souplet, Philippe 8 2020 The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients. Zbl 1471.35138 Sirakov, Boyan; Souplet, Philippe 8 2021 Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with \(p\)-Laplacian diffusion. Zbl 1353.35070 Attouchi, Amal; Souplet, Philippe 7 2017 Critical exponents, special large-time behavior and oscillatory blow-up in nonlinear ODE’s. Zbl 1015.34038 Souplet, Philippe 7 1998 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 7 1995 Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations. Zbl 1448.35051 Attouchi, Amal; Souplet, Philippe 7 2020 Existence of exceptional growing-up solutions for a class of nonlinear second order ordinary differential equations. Zbl 0849.34024 Souplet, Philippe 6 1995 A survey on \(L^p_\delta\) spaces and their applications to nonlinear elliptic and parabolic problems. Zbl 1080.35026 Souplet, Philippe 6 2004 Oscillatory blow-up in nonlinear second order ODE’s: The critical case. Zbl 1048.34074 Balabane, Mikhaël; Jazar, Mustapha; Souplet, Philippe 6 2003 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 5 2011 A priori estimates of global solutions of superlinear parabolic problems without variational structure. Zbl 1029.35049 Quittner, Pavol; Souplet, Philippe 5 2003 A priori and universal estimates for global solutions of superlinear degenerate parabolic equations. Zbl 1072.35099 Souplet, Philippe 5 2002 Blow-up rate of solutions of parabolic problems with nonlinear boundary conditions. Zbl 1364.35175 Quittner, Pavol; Souplet, Philippe 5 2012 No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem. Zbl 1444.35104 Esteve, Carlos; Souplet, Philippe 5 2019 Self-similar subsolutions and blow-up for nonlinear parabolic equations. Zbl 0893.35056 Souplet, Philippe; Weissler, Fred B. 4 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 4 1991 Global existence from single-component \(L_{p}\) estimates in a semilinear reaction-diffusion system. Zbl 0993.35048 Quittner, Pavol; Souplet, Philippe 4 2002 A simplified approach to the refined blowup behavior for the nonlinear heat equation. Zbl 1411.35176 Souplet, Philippe 4 2019 Optimal growth rates for a viscous Hamilton-Jacobi equation. Zbl 1090.35036 Laurençot, Philippe; Souplet, Philippe 4 2005 Universal estimates and Liouville theorems for superlinear problems without scale invariance. Zbl 1518.35344 Souplet, Philippe 3 2023 Singularity formation and regularization at multiple times in the viscous Hamilton-Jacobi equation. Zbl 1529.35401 Mizoguchi, Noriko; Souplet, Philippe 1 2023 A Liouville-type theorem for the Lane-Emden equation in a half-space. Zbl 1491.35089 Dupaigne, Louis; Sirakov, Boyan; Souplet, Philippe 8 2022 The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients. Zbl 1471.35138 Sirakov, Boyan; Souplet, Philippe 8 2021 Sharp condition for the Liouville property in a class of nonlinear elliptic inequalities. Zbl 1467.35151 Souplet, Philippe 1 2021 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 16 2020 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 14 2020 A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient. Zbl 1440.35106 Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe 10 2020 Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities. Zbl 1439.35199 Jleli, Mohamed; Samet, Bessem; Souplet, Philippe 8 2020 Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations. Zbl 1448.35051 Attouchi, Amal; Souplet, Philippe 7 2020 Superlinear parabolic problems. Blow-up, global existence and steady states. 2nd revised and updated edition. Zbl 1423.35004 Quittner, Pavol; Souplet, Philippe 139 2019 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140 Souplet, Philippe; Winkler, Michael 42 2019 Optimal condition for blow-up of the critical \(L^q\) norm for the semilinear heat equation. Zbl 1420.35139 Mizoguchi, Noriko; Souplet, Philippe 11 2019 No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem. Zbl 1444.35104 Esteve, Carlos; Souplet, Philippe 5 2019 A simplified approach to the refined blowup behavior for the nonlinear heat equation. Zbl 1411.35176 Souplet, Philippe 4 2019 Corrigendum to: “Nondegeneracy of blow-up points for the parabolic Keller-Segel system”. Zbl 1415.35062 Mizoguchi, N.; Souplet, Ph. 4 2019 Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth. Zbl 1516.35235 Souplet, Philippe 26 2018 Excluding blowup at zero points of the potential by means of Liouville-type theorems. Zbl 1394.35229 Guo, Jong-Shenq; Souplet, Philippe 13 2018 Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity. Zbl 1397.35127 Esteve, Carlos; Souplet, Philippe 4 2018 Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in \(\mathbb{R}^n\). Zbl 1372.35157 Souplet, Philippe 19 2017 Analysis of the loss of boundary conditions for the diffusive Hamilton-Jacobi equation. Zbl 1391.35078 Porretta, Alessio; Souplet, Philippe 17 2017 The profile of boundary gradient blowup for the diffusive Hamilton-Jacobi equation. Zbl 1405.35097 Porretta, Alessio; Souplet, Philippe 16 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 7 2017 A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems. Zbl 1362.35063 Phan, Quoc Hung; Souplet, Philippe 11 2016 Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. Zbl 1383.35098 Souplet, Philippe; Tayachi, Slim 8 2016 No touchdown at zero points of the permittivity profile for the MEMS problem. Zbl 1332.35160 Guo, Jong-Shenq; Souplet, Philippe 16 2015 Improved conditions for single-point blow-up in reaction-diffusion systems. Zbl 1320.35097 Mahmoudi, Nejib; Souplet, Philippe; Tayachi, Slim 15 2015 A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient. Zbl 1318.35018 Souplet, Philippe 8 2015 Nondegeneracy of blow-up points for the parabolic Keller-Segel system. Zbl 1302.35075 Mizoguchi, Noriko; Souplet, Philippe 219 2014 Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems. Zbl 1298.35060 Montaru, Alexandre; Sirakov, Boyan; Souplet, Philippe 17 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 2 2014 Global existence of solutions for a chemotaxis-type system arising in crime modelling. Zbl 1284.35445 Manásevich, Raúl; Phan Quoc Hung; Souplet, Philippe 32 2013 Liouville-type theorems and bounds of solutions of Hardy-Hénon equations. Zbl 1233.35093 Phan Quoc Hung; Souplet, Philippe 83 2012 Symmetry of components for semilinear elliptic systems. Zbl 1255.35111 Quittner, Pavol; Souplet, Philippe 35 2012 Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications. Zbl 1254.35077 Quittner, Pavol; Souplet, Philippe 29 2012 Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices. Zbl 1263.35100 Souplet, Philippe 8 2012 Blow-up rate of solutions of parabolic problems with nonlinear boundary conditions. Zbl 1364.35175 Quittner, Pavol; Souplet, Philippe 5 2012 Classification of large-time behaviors in a reaction-diffusion system modeling diallelic selection. Zbl 1319.92032 Souplet, Philippe; Winkler, Michael 1 2012 Transversality of stable and Nehari manifolds for a semilinear heat equation. Zbl 1233.35045 Dickstein, Flavio; Mizoguchi, Noriko; Souplet, Philippe; Weissler, Fred 16 2011 Parabolic Liouville-type theorems via their elliptic counterparts. Zbl 1306.35066 Quittner, Pavol; Souplet, Philippe 11 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 5 2011 Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains. Zbl 1218.35052 Yuxiang, Li; Souplet, Philippe 32 2010 Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Zbl 1195.35077 Ammar, Kaouther; Souplet, Philippe 11 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 9 2010 The proof of the Lane-Emden conjecture in four space dimensions. Zbl 1171.35035 Souplet, Philippe 169 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 26 2009 Single-point blow-up for a semilinear parabolic system. Zbl 1171.35059 Souplet, Philippe 21 2009 An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source. Zbl 1172.35038 Souplet, Philippe 9 2009 Superlinear parabolic problems. Blow-up, global existence and steady states. Zbl 1128.35003 Quittner, Pavol; Souplet, Philippe 689 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 254 2007 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051 Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 91 2007 A note on diffusion-induced blow-up. Zbl 1145.35068 Souplet, Philippe 4 2007 A remark on the large time behavior of solutions of viscous Hamilton-Jacobi equations. Zbl 1134.35019 Souplet, Philippe 1 2007 Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds. Zbl 1109.58025 Souplet, Philippe; Zhang, Qi S. 141 2006 Global solutions of inhomogeneous Hamilton-Jacobi equations. Zbl 1149.35050 Souplet, Philippe; Zhang, Qi S. 47 2006 Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. Zbl 1116.35070 Souplet, Philippe; Vázquez, Juan Luis 23 2006 Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system. Zbl 1212.35219 Rossi, Julio D.; Souplet, Philippe 43 2005 Optimal regularity conditions for elliptic problems via \(L^p_\delta\)-spaces. Zbl 1130.35057 Souplet, Philippe 21 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 18 2005 The influence of gradient perturbations on blow-up asymptotics in semilinear parabolic problems: a survey. Zbl 1094.35060 Souplet, Philippe 9 2005 Optimal growth rates for a viscous Hamilton-Jacobi equation. Zbl 1090.35036 Laurençot, Philippe; Souplet, Philippe 4 2005 A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces. Zbl 1113.35062 Quittner, P.; Souplet, Ph. 49 2004 Optimal condition for non-simultaneous blow-up in a reaction-diffusion system. Zbl 1059.35049 Souplet, Philippe; Tayachi, Slim 48 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 26 2004 Uniform blow up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping. Zbl 1058.35121 Souplet, Philippe 23 2004 Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory. Zbl 1099.35049 Souplet, Philippe 22 2004 Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027 Quittner, Pavol; Souplet, Philippe; Winkler, Michael 19 2004 An example of uniformly recurrent function which is not almost periodic. Zbl 1051.42008 Haraux, Alain; Souplet, Philippe 10 2004 A survey on \(L^p_\delta\) spaces and their applications to nonlinear elliptic and parabolic problems. Zbl 1080.35026 Souplet, Philippe 6 2004 Instantaneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations. Zbl 1052.35090 Matos, Júlia; Souplet, Philippe 3 2004 Gradient bounds for solutions of semilinear parabolic equations without Bernstein’s quadratic condition. Zbl 1073.35045 Bartier, Jean-Philippe; Souplet, Philippe 2 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. 24 2003 On the growth of mass for a viscous Hamilton-Jacobi equation. Zbl 1031.35054 Laurençot, Philippe; Souplet, Philippe 19 2003 Universal blow-up rates for a semilinear heat equation and applications. Zbl 1028.35065 Matos, Júlia; Souplet, Philippe 16 2003 Bounds of global solutions of parabolic problems with nonlinear boundary conditions. Zbl 1080.35039 Quittner, Pavol; Souplet, Philippe 8 2003 Oscillatory blow-up in nonlinear second order ODE’s: The critical case. Zbl 1048.34074 Balabane, Mikhaël; Jazar, Mustapha; Souplet, Philippe 6 2003 A priori estimates of global solutions of superlinear parabolic problems without variational structure. Zbl 1029.35049 Quittner, Pavol; Souplet, Philippe 5 2003 The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces. Zbl 1046.35046 Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B. 67 2002 Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions. Zbl 1015.35016 Souplet, Philippe 48 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. 20 2002 Critical blowup exponents for a system of reaction-diffusion equations with absorption. Zbl 0996.35029 Bedjaoui, Nabil; Souplet, Philippe 19 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. 15 2002 Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations. Zbl 1007.35040 Souplet, Philippe 13 2002 A priori and universal estimates for global solutions of superlinear degenerate parabolic equations. Zbl 1072.35099 Souplet, Philippe 5 2002 Global existence from single-component \(L_{p}\) estimates in a semilinear reaction-diffusion system. Zbl 0993.35048 Quittner, Pavol; Souplet, Philippe 4 2002 Recent results and open problems on parabolic equations with gradient nonlinearities. Zbl 0982.35054 Souplet, Philippe 40 2001 Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103 Fila, Marek; Souplet, Philippe 34 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. 31 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 30 2001 The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046 Fila, Marek; Souplet, Philippe 28 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 16 2001 Blowup rates for nonlinear heat equations with gradient terms and for parabolic inequalities. Zbl 0984.35077 Souplet, Philippe; Tayachi, Slim 15 2001 Existence of ground states for semilinear elliptic equations with decaying mass: A parabolic approach. Zbl 0992.35029 Souplet, Philippe; Zhang, Qi S. 1 2001 Decay of heat semigroups in \(L^\infty\) and applications to nonlinear parabolic problems in unbounded domains. Zbl 0954.35032 Souplet, Philippe 12 2000 Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079 Martel, Yvan; Souplet, Philippe 8 2000 Blow-up behavior in nonlocal vs. local heat equations. Zbl 0954.35091 Souplet, Philippe 1 2000 Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source. Zbl 0923.35077 Souplet, Philippe 160 1999 Poincaré’s inequality and global solutions of a nonlinear parabolic equation. Zbl 0924.35065 Souplet, Philippe; Weissler, Fred B. 18 1999 Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations. Zbl 0926.35064 Souplet, Philippe 17 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. 12 1999 ...and 17 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,115 Authors 64 Winkler, Michael 57 Souplet, Philippe 53 Mu, Chunlai 33 Liu, Bingchen 32 Zheng, Sining 30 Li, Fengjie 29 Ishige, Kazuhiro 28 Fang, Zhongbo 27 Wei, Juncheng 24 Li, Yuxiang 22 Zhang, Zhengce 21 Iagar, Razvan Gabriel 19 Laurençot, Philippe 19 Quittner, Pavol 19 Xiang, Zhaoyin 18 Ding, Juntang 18 Lankeit, Johannes 17 Duong, Anh Tuan 17 Fujishima, Yohei 17 Kawakami, Tatsuki 17 Zheng, Pan 17 Zhou, Jun 15 Wang, Liangchen 15 Weissler, Fred B. 15 Xie, Chunhong 14 Tang, Bao Quoc 14 Zaag, Hatem 14 Zou, Wenming 13 Guo, Zongming 13 Jin, Haiyang 13 Mizoguchi, Noriko 13 Quaas, Alexander 13 Sánchez, Ariel 13 Yanagida, Eiji 12 Fila, Marek 12 Lin, Zhigui 12 Phan, Quoc Hung 12 Wang, Mingxin 12 Wang, Yulan 11 García-Melián, Jorge 11 Ghergu, Marius 11 Harrabi, Abdellaziz 11 Liu, Qilin 11 Parshad, Rana D. 11 Tayachi, Slim 11 Villavert, John 11 Yin, Jingxue 11 Zhang, Zhitao 10 Karch, Grzegorz 10 Liu, Bin 10 Ma, Li 10 Tao, Youshan 10 Wan, FangShu 10 Wang, Wei 10 Weth, Tobias 10 Yang, Zuodong 9 Bidaut-Veron, Marie-Françoise 9 Biler, Piotr 9 Cowan, Craig 9 Dai, Wei 9 Del Pino, Manuel A. 9 Fellner, Klemens 9 Gao, Wenjie 9 Guo, Jong-Shenq 9 Lei, Yutian 9 Liu, Dengming 9 Musso, Monica 9 Nguyễn Thạc Dũng 9 Poláčik, Peter 9 Punzo, Fabio 9 Rodríguez-Bernal, Aníbal 9 Song, Xianfa 9 Stinner, Christian 9 Takahashi, Jin 9 Taliaferro, Steven D. 9 Vernier-Piro, Stella 9 Wang, Wen 8 Deng, Weibing 8 Díaz Díaz, Jesús Ildefonso 8 Du, Lili 8 Ferreira, Raúl 8 Harada, Junichi 8 Kirane, Mokhtar 8 Kong, Linghua 8 Kostić, Marko 8 Loayza, Miguel 8 Miyamoto, Yasuhito 8 Morgan, Jeff J. 8 Rahal, Belgacem 8 Samet, Bessem 8 Sierżȩga, Mikołaj 8 Sirakov, Boyan Slavchev 8 Sun, Yuhua 8 Torebek, Berikbol Tillabayuly 8 Wang, Xiaoliu 8 Wu, Jiayong 8 Yang, Hui 8 Yokota, Tomomi 7 Abdellaoui, Boumediene 7 Abolarinwa, Abimbola ...and 2,015 more Authors all top 5 Cited in 277 Serials 195 Journal of Differential Equations 174 Journal of Mathematical Analysis and Applications 168 Nonlinear Analysis. 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Series B (English Edition) 6 Journal of Applied Mathematics and Computing 6 Evolution Equations and Control Theory 6 Journal of Function Spaces 6 Open Mathematics 6 AIMS Mathematics 6 Mathematics in Engineering 6 Electronic Research Archive 5 Israel Journal of Mathematics 5 Manuscripta Mathematica 5 Quarterly of Applied Mathematics 5 Studies in Applied Mathematics 5 Bulletin of the Iranian Mathematical Society 5 Mathematical and Computer Modelling 5 Turkish Journal of Mathematics 5 Bulletin des Sciences Mathématiques 5 Revista Matemática Complutense 5 Milan Journal of Mathematics 5 Advances in Difference Equations 4 Mathematical Notes 4 Journal of Geometry and Physics 4 Applied Mathematics and Optimization 4 Bulletin of the London Mathematical Society 4 Duke Mathematical Journal 4 Journal of the Mathematical Society of Japan 4 Pacific Journal of Mathematics 4 Results in Mathematics 4 Tôhoku Mathematical Journal. 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