Edit Profile (opens in new tab) Souplet, Philippe Co-Author Distance Author ID: souplet.philippe Published as: Souplet, Philippe; Souplet, Ph. Documents Indexed: 124 Publications since 1991, including 2 Books Co-Authors: 45 Co-Authors with 81 Joint Publications 1,152 Co-Co-Authors all top 5 Co-Authors 43 single-authored 14 Quittner, Pavol 9 Weissler, Fred B. 6 Mizoguchi, Noriko 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 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 Ioannis 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 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 117 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 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 114 Publications have been cited 3,220 times in 1,943 Documents Cited by ▼ Year ▼ Superlinear parabolic problems. Blow-up, global existence and steady states. Zbl 1128.35003Quittner, Pavol; Souplet, Philippe 568 2007 Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 212 2007 Blow-up in nonlocal reaction-diffusion equations. Zbl 0909.35073Souplet, Philippe 164 1998 Nondegeneracy of blow-up points for the parabolic Keller-Segel system. Zbl 1302.35075Mizoguchi, Noriko; Souplet, Philippe 158 2014 Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source. Zbl 0923.35077Souplet, Philippe 157 1999 The proof of the Lane-Emden conjecture in four space dimensions. Zbl 1171.35035Souplet, Philippe 146 2009 Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds. Zbl 1109.58025Souplet, Philippe; Zhang, Qi S. 114 2006 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 74 2007 Liouville-type theorems and bounds of solutions of Hardy-Hénon equations. Zbl 1233.35093Phan Quoc Hung; Souplet, Philippe 71 2012 Superlinear parabolic problems. Blow-up, global existence and steady states. 2nd revised and updated edition. Zbl 1423.35004Quittner, Pavol; Souplet, Philippe 68 2019 The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces. Zbl 1046.35046Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B. 62 2002 Finite time blow-up for a nonlinear parabolic equation with a gradient term and applications. Zbl 0858.35067Souplet, Philippe 56 1996 Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions. Zbl 1015.35016Souplet, Philippe 46 2002 A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces. Zbl 1113.35062Quittner, P.; Souplet, Ph. 45 2004 Optimal condition for non-simultaneous blow-up in a reaction-diffusion system. Zbl 1059.35049Souplet, Philippe; Tayachi, Slim 44 2004 Global solutions of inhomogeneous Hamilton-Jacobi equations. Zbl 1149.35050Souplet, Philippe; Zhang, Qi S. 42 2006 Self-similar subsolutions and blowup for nonlinear parabolic equations. Zbl 0892.35011Souplet, Philippe; Weissler, Fred B. 42 1997 Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system. Zbl 1212.35219Rossi, Julio D.; Souplet, Philippe 39 2005 Recent results and open problems on parabolic equations with gradient nonlinearities. Zbl 0982.35054Souplet, Philippe 37 2001 Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains. Zbl 1218.35052Yuxiang, Li; Souplet, Philippe 31 2010 Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103Fila, Marek; Souplet, Philippe 29 2001 Linear and nonlinear heat equations in \(L^q_\delta\) spaces and universal bounds for global solutions. Zbl 0993.35023Fila, Marek; Souplet, Philippe; Weissler, Fred B. 29 2001 Symmetry of components for semilinear elliptic systems. Zbl 1255.35111Quittner, Pavol; Souplet, Philippe 29 2012 Decay of global solutions, stability and blow up for a reaction-diffusion problem with free boundary. Zbl 0959.35087Ghidouche, Hamid; Souplet, Philippe; Tarzia, Domingo 27 2001 The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046Fila, Marek; Souplet, Philippe 26 2001 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140Souplet, Philippe; Winkler, Michael 25 2019 Global existence of solutions for a chemotaxis-type system arising in crime modelling. Zbl 1284.35445Manásevich, Raúl; Phan Quoc Hung; Souplet, Philippe 25 2013 Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena. Zbl 1072.35098Rodriguez-Bernal, Anibal; Arrieta, José M.; Souplet, Philippe 24 2004 Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications. Zbl 1254.35077Quittner, Pavol; Souplet, Philippe 24 2012 Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk. Zbl 1387.35354Kavallaris, Nikos I.; Souplet, Philippe 23 2009 Uniform blow up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping. Zbl 1058.35121Souplet, Philippe 22 2004 Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. Zbl 1116.35070Souplet, Philippe; Vázquez, Juan Luis 22 2006 Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state. Zbl 1029.35106Souplet, Philippe; Weissler, Fred B. 21 2003 Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory. Zbl 1099.35049Souplet, Philippe 20 2004 Critical blowup exponents for a system of reaction-diffusion equations with absorption. Zbl 0996.35029Bedjaoui, Nabil; Souplet, Philippe 19 2002 Single-point blow-up for a semilinear parabolic system. Zbl 1171.35059Souplet, Philippe 19 2009 Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027Quittner, Pavol; Souplet, Philippe; Winkler, Michael 19 2004 Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term. Zbl 0990.35061Souplet, Philippe; Tayachi, Slim; Weissler, Fred B. 19 1996 Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations. Zbl 0892.35078Souplet, Philippe 19 1998 Optimal regularity conditions for elliptic problems via \(L^p_\delta\)-spaces. Zbl 1130.35057Souplet, Philippe 18 2005 Poincaré’s inequality and global solutions of a nonlinear parabolic equation. Zbl 0924.35065Souplet, Philippe; Weissler, Fred B. 18 1999 Extinction and non-extinction for viscous Hamilton-Jacobi equations in \(\mathbb{R}^N\). Zbl 1046.35053Benachour, S.; Laurençot, Ph.; Schmitt, D.; Souplet, Ph. 18 2002 On the growth of mass for a viscous Hamilton-Jacobi equation. Zbl 1031.35054Laurençot, Philippe; Souplet, Philippe 18 2003 Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up. Zbl 1063.35087Guo, Jong-Shenq; Souplet, Philippe 17 2005 Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems. Zbl 1298.35060Montaru, Alexandre; Sirakov, Boyan; Souplet, Philippe 17 2014 Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth. Zbl 1516.35235Souplet, Philippe 17 2018 Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations. Zbl 0926.35064Souplet, Philippe 16 1999 Uniqueness and nonuniqueness results for the antiperiodic solutions of some second-order nonlinear evolution equations. Zbl 0855.34075Souplet, Philippe 16 1996 Analysis of the loss of boundary conditions for the diffusive Hamilton-Jacobi equation. Zbl 1391.35078Porretta, Alessio; Souplet, Philippe 16 2017 Admissible \(L_p\) norms for local existence and for continuation in semilinear parabolic systems are not the same. Zbl 1006.35048Quittner, Pavol; Souplet, Philippe 15 2001 Universal blow-up rates for a semilinear heat equation and applications. Zbl 1028.35065Matos, Júlia; Souplet, Philippe 15 2003 Transversality of stable and Nehari manifolds for a semilinear heat equation. Zbl 1233.35045Dickstein, Flavio; Mizoguchi, Noriko; Souplet, Philippe; Weissler, Fred 15 2011 Blowup rates for nonlinear heat equations with gradient terms and for parabolic inequalities. Zbl 0984.35077Souplet, Philippe; Tayachi, Slim 15 2001 The profile of boundary gradient blowup for the diffusive Hamilton-Jacobi equation. Zbl 1405.35097Porretta, Alessio; Souplet, Philippe 15 2017 No touchdown at zero points of the permittivity profile for the MEMS problem. Zbl 1332.35160Guo, Jong-Shenq; Souplet, Philippe 14 2015 Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in \(\mathbb{R}^n\). Zbl 1372.35157Souplet, Philippe 14 2017 Improved conditions for single-point blow-up in reaction-diffusion systems. Zbl 1320.35097Mahmoudi, Nejib; Souplet, Philippe; Tayachi, Slim 13 2015 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 0938.35068Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B. 12 1999 Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations. Zbl 1007.35040Souplet, Philippe 12 2002 Decay of heat semigroups in \(L^\infty\) and applications to nonlinear parabolic problems in unbounded domains. Zbl 0954.35032Souplet, Philippe 11 2000 Stability for semilinear parabolic equations with decaying potentials in \(\mathbb{R}^n\) and dynamical approach to the existence of ground states. Zbl 1017.35033Souplet, Philippe; Zhang, Qi S. 11 2002 Nonexistence of global solutions to some differential inequalities of the second order and applications. Zbl 0843.34017Souplet, Philippe 11 1995 A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton-Jacobi equations. Zbl 1436.35010Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe 11 2020 Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation. Zbl 1437.35112Porretta, Alessio; Souplet, Philippe 11 2020 Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Zbl 1195.35077Ammar, Kaouther; Souplet, Philippe 10 2010 Parabolic Liouville-type theorems via their elliptic counterparts. Zbl 1306.35066Quittner, Pavol; Souplet, Philippe 10 2011 Excluding blowup at zero points of the potential by means of Liouville-type theorems. Zbl 1394.35229Guo, Jong-Shenq; Souplet, Philippe 9 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 0860.35051Souplet, Philippe 8 1996 A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient. Zbl 1318.35018Souplet, Philippe 8 2015 Bounds of global solutions of parabolic problems with nonlinear boundary conditions. Zbl 1080.35039Quittner, Pavol; Souplet, Philippe 7 2003 Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079Martel, Yvan; Souplet, Philippe 7 2000 Non-self-similar dead-core rate for the fast diffusion equation with strong absorption. Zbl 1194.35059Guo, Jong-Shenq; Ling, Chia-Tung; Souplet, Philippe 7 2010 Finite time blow up for a nonlinear heat equation. (Résultats d’explosion en temps fini pour une équation de la chaleur non linéaire.) Zbl 0843.35044Souplet, Philippe 7 1995 An example of uniformly recurrent function which is not almost periodic. Zbl 1051.42008Haraux, Alain; Souplet, Philippe 7 2004 Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices. Zbl 1263.35100Souplet, Philippe 7 2012 Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. Zbl 1383.35098Souplet, Philippe; Tayachi, Slim 7 2016 Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with \(p\)-Laplacian diffusion. Zbl 1353.35070Attouchi, Amal; Souplet, Philippe 7 2017 A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems. Zbl 1362.35063Phan, Quoc Hung; Souplet, Philippe 7 2016 The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients. Zbl 1471.35138Sirakov, Boyan; Souplet, Philippe 7 2021 The influence of gradient perturbations on blow-up asymptotics in semilinear parabolic problems: a survey. Zbl 1094.35060Souplet, Philippe 6 2005 Critical exponents, special large-time behavior and oscillatory blow-up in nonlinear ODE’s. Zbl 1015.34038Souplet, Philippe 6 1998 A survey on \(L^p_\delta\) spaces and their applications to nonlinear elliptic and parabolic problems. Zbl 1080.35026Souplet, Philippe 6 2004 An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source. Zbl 1172.35038Souplet, Philippe 6 2009 Oscillatory blow-up in nonlinear second order ODE’s: The critical case. Zbl 1048.34074Balabane, Mikhaël; Jazar, Mustapha; Souplet, Philippe 6 2003 Existence of exceptional growing-up solutions for a class of nonlinear second order ordinary differential equations. Zbl 0849.34024Souplet, Philippe 6 1995 Optimal condition for blow-up of the critical \(L^q\) norm for the semilinear heat equation. Zbl 1420.35139Mizoguchi, Noriko; Souplet, Philippe 6 2019 A priori and universal estimates for global solutions of superlinear degenerate parabolic equations. Zbl 1072.35099Souplet, Philippe 5 2002 A priori estimates of global solutions of superlinear parabolic problems without variational structure. Zbl 1029.35049Quittner, Pavol; Souplet, Philippe 5 2003 Blow-up rate of solutions of parabolic problems with nonlinear boundary conditions. Zbl 1364.35175Quittner, Pavol; Souplet, Philippe 5 2012 Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations. Zbl 1448.35051Attouchi, Amal; Souplet, Philippe 5 2020 A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient. Zbl 1440.35106Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe 5 2020 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 0738.34003Souplet, Philippe 4 1991 A note on diffusion-induced blow-up. Zbl 1145.35068Souplet, Philippe 4 2007 Self-similar subsolutions and blow-up for nonlinear parabolic equations. Zbl 0893.35056Souplet, Philippe; Weissler, Fred B. 4 1997 The influence of space dimension on the large-time behavior in a reaction-diffusion system modeling diallelic selection. Zbl 1303.92086Souplet, Philippe; Winkler, Michael 4 2011 A Liouville-type theorem for the Lane-Emden equation in a half-space. Zbl 1491.35089Dupaigne, Louis; Sirakov, Boyan; Souplet, Philippe 4 2022 Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities. Zbl 1439.35199Jleli, Mohamed; Samet, Bessem; Souplet, Philippe 4 2020 Optimal growth rates for a viscous Hamilton-Jacobi equation. Zbl 1090.35036Laurençot, Philippe; Souplet, Philippe 3 2005 Global existence from single-component \(L_{p}\) estimates in a semilinear reaction-diffusion system. Zbl 0993.35048Quittner, Pavol; Souplet, Philippe 3 2002 Corrigendum to: “Nondegeneracy of blow-up points for the parabolic Keller-Segel system”. Zbl 1415.35062Mizoguchi, N.; Souplet, Ph. 3 2019 A Liouville-type theorem for the Lane-Emden equation in a half-space. Zbl 1491.35089Dupaigne, Louis; Sirakov, Boyan; Souplet, Philippe 4 2022 The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients. Zbl 1471.35138Sirakov, Boyan; Souplet, Philippe 7 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 1436.35010Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe 11 2020 Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation. Zbl 1437.35112Porretta, Alessio; Souplet, Philippe 11 2020 Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations. Zbl 1448.35051Attouchi, Amal; Souplet, Philippe 5 2020 A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient. Zbl 1440.35106Filippucci, Roberta; Pucci, Patrizia; Souplet, Philippe 5 2020 Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities. Zbl 1439.35199Jleli, Mohamed; Samet, Bessem; Souplet, Philippe 4 2020 Superlinear parabolic problems. Blow-up, global existence and steady states. 2nd revised and updated edition. Zbl 1423.35004Quittner, Pavol; Souplet, Philippe 68 2019 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140Souplet, Philippe; Winkler, Michael 25 2019 Optimal condition for blow-up of the critical \(L^q\) norm for the semilinear heat equation. Zbl 1420.35139Mizoguchi, Noriko; Souplet, Philippe 6 2019 Corrigendum to: “Nondegeneracy of blow-up points for the parabolic Keller-Segel system”. Zbl 1415.35062Mizoguchi, N.; Souplet, Ph. 3 2019 A simplified approach to the refined blowup behavior for the nonlinear heat equation. Zbl 1411.35176Souplet, Philippe 3 2019 No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem. Zbl 1444.35104Esteve, Carlos; Souplet, Philippe 2 2019 Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth. Zbl 1516.35235Souplet, Philippe 17 2018 Excluding blowup at zero points of the potential by means of Liouville-type theorems. Zbl 1394.35229Guo, Jong-Shenq; Souplet, Philippe 9 2018 Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity. Zbl 1397.35127Esteve, Carlos; Souplet, Philippe 1 2018 Analysis of the loss of boundary conditions for the diffusive Hamilton-Jacobi equation. Zbl 1391.35078Porretta, Alessio; Souplet, Philippe 16 2017 The profile of boundary gradient blowup for the diffusive Hamilton-Jacobi equation. Zbl 1405.35097Porretta, Alessio; Souplet, Philippe 15 2017 Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in \(\mathbb{R}^n\). Zbl 1372.35157Souplet, Philippe 14 2017 Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with \(p\)-Laplacian diffusion. Zbl 1353.35070Attouchi, Amal; Souplet, Philippe 7 2017 Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. Zbl 1383.35098Souplet, Philippe; Tayachi, Slim 7 2016 A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems. Zbl 1362.35063Phan, Quoc Hung; Souplet, Philippe 7 2016 No touchdown at zero points of the permittivity profile for the MEMS problem. Zbl 1332.35160Guo, Jong-Shenq; Souplet, Philippe 14 2015 Improved conditions for single-point blow-up in reaction-diffusion systems. Zbl 1320.35097Mahmoudi, Nejib; Souplet, Philippe; Tayachi, Slim 13 2015 A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient. Zbl 1318.35018Souplet, Philippe 8 2015 Nondegeneracy of blow-up points for the parabolic Keller-Segel system. Zbl 1302.35075Mizoguchi, Noriko; Souplet, Philippe 158 2014 Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems. Zbl 1298.35060Montaru, 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 1300.35032Montaru, Alexandre; Souplet, Philippe 2 2014 Global existence of solutions for a chemotaxis-type system arising in crime modelling. Zbl 1284.35445Manásevich, Raúl; Phan Quoc Hung; Souplet, Philippe 25 2013 Liouville-type theorems and bounds of solutions of Hardy-Hénon equations. Zbl 1233.35093Phan Quoc Hung; Souplet, Philippe 71 2012 Symmetry of components for semilinear elliptic systems. Zbl 1255.35111Quittner, Pavol; Souplet, Philippe 29 2012 Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications. Zbl 1254.35077Quittner, Pavol; Souplet, Philippe 24 2012 Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices. Zbl 1263.35100Souplet, Philippe 7 2012 Blow-up rate of solutions of parabolic problems with nonlinear boundary conditions. Zbl 1364.35175Quittner, Pavol; Souplet, Philippe 5 2012 Classification of large-time behaviors in a reaction-diffusion system modeling diallelic selection. Zbl 1319.92032Souplet, Philippe; Winkler, Michael 1 2012 Transversality of stable and Nehari manifolds for a semilinear heat equation. Zbl 1233.35045Dickstein, Flavio; Mizoguchi, Noriko; Souplet, Philippe; Weissler, Fred 15 2011 Parabolic Liouville-type theorems via their elliptic counterparts. Zbl 1306.35066Quittner, Pavol; Souplet, Philippe 10 2011 The influence of space dimension on the large-time behavior in a reaction-diffusion system modeling diallelic selection. Zbl 1303.92086Souplet, Philippe; Winkler, Michael 4 2011 Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains. Zbl 1218.35052Yuxiang, Li; Souplet, Philippe 31 2010 Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Zbl 1195.35077Ammar, Kaouther; Souplet, Philippe 10 2010 Non-self-similar dead-core rate for the fast diffusion equation with strong absorption. Zbl 1194.35059Guo, Jong-Shenq; Ling, Chia-Tung; Souplet, Philippe 7 2010 The proof of the Lane-Emden conjecture in four space dimensions. Zbl 1171.35035Souplet, Philippe 146 2009 Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk. Zbl 1387.35354Kavallaris, Nikos I.; Souplet, Philippe 23 2009 Single-point blow-up for a semilinear parabolic system. Zbl 1171.35059Souplet, Philippe 19 2009 An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source. Zbl 1172.35038Souplet, Philippe 6 2009 Superlinear parabolic problems. Blow-up, global existence and steady states. Zbl 1128.35003Quittner, Pavol; Souplet, Philippe 568 2007 Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 212 2007 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 74 2007 A note on diffusion-induced blow-up. Zbl 1145.35068Souplet, Philippe 4 2007 A remark on the large time behavior of solutions of viscous Hamilton-Jacobi equations. Zbl 1134.35019Souplet, Philippe 1 2007 Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds. Zbl 1109.58025Souplet, Philippe; Zhang, Qi S. 114 2006 Global solutions of inhomogeneous Hamilton-Jacobi equations. Zbl 1149.35050Souplet, Philippe; Zhang, Qi S. 42 2006 Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. Zbl 1116.35070Souplet, Philippe; Vázquez, Juan Luis 22 2006 Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system. Zbl 1212.35219Rossi, Julio D.; Souplet, Philippe 39 2005 Optimal regularity conditions for elliptic problems via \(L^p_\delta\)-spaces. Zbl 1130.35057Souplet, Philippe 18 2005 Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up. Zbl 1063.35087Guo, Jong-Shenq; Souplet, Philippe 17 2005 The influence of gradient perturbations on blow-up asymptotics in semilinear parabolic problems: a survey. Zbl 1094.35060Souplet, Philippe 6 2005 Optimal growth rates for a viscous Hamilton-Jacobi equation. Zbl 1090.35036Laurençot, Philippe; Souplet, Philippe 3 2005 A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces. Zbl 1113.35062Quittner, P.; Souplet, Ph. 45 2004 Optimal condition for non-simultaneous blow-up in a reaction-diffusion system. Zbl 1059.35049Souplet, Philippe; Tayachi, Slim 44 2004 Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena. Zbl 1072.35098Rodriguez-Bernal, Anibal; Arrieta, José M.; Souplet, Philippe 24 2004 Uniform blow up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping. Zbl 1058.35121Souplet, Philippe 22 2004 Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory. Zbl 1099.35049Souplet, Philippe 20 2004 Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027Quittner, Pavol; Souplet, Philippe; Winkler, Michael 19 2004 An example of uniformly recurrent function which is not almost periodic. Zbl 1051.42008Haraux, Alain; Souplet, Philippe 7 2004 A survey on \(L^p_\delta\) spaces and their applications to nonlinear elliptic and parabolic problems. Zbl 1080.35026Souplet, Philippe 6 2004 Instantaneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations. Zbl 1052.35090Matos, Júlia; Souplet, Philippe 2 2004 Gradient bounds for solutions of semilinear parabolic equations without Bernstein’s quadratic condition. Zbl 1073.35045Bartier, Jean-Philippe; Souplet, Philippe 2 2004 Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state. Zbl 1029.35106Souplet, Philippe; Weissler, Fred B. 21 2003 On the growth of mass for a viscous Hamilton-Jacobi equation. Zbl 1031.35054Laurençot, Philippe; Souplet, Philippe 18 2003 Universal blow-up rates for a semilinear heat equation and applications. Zbl 1028.35065Matos, Júlia; Souplet, Philippe 15 2003 Bounds of global solutions of parabolic problems with nonlinear boundary conditions. Zbl 1080.35039Quittner, Pavol; Souplet, Philippe 7 2003 Oscillatory blow-up in nonlinear second order ODE’s: The critical case. Zbl 1048.34074Balabane, Mikhaël; Jazar, Mustapha; Souplet, Philippe 6 2003 A priori estimates of global solutions of superlinear parabolic problems without variational structure. Zbl 1029.35049Quittner, Pavol; Souplet, Philippe 5 2003 The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces. Zbl 1046.35046Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B. 62 2002 Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions. Zbl 1015.35016Souplet, Philippe 46 2002 Critical blowup exponents for a system of reaction-diffusion equations with absorption. Zbl 0996.35029Bedjaoui, Nabil; Souplet, Philippe 19 2002 Extinction and non-extinction for viscous Hamilton-Jacobi equations in \(\mathbb{R}^N\). Zbl 1046.35053Benachour, S.; Laurençot, Ph.; Schmitt, D.; Souplet, Ph. 18 2002 Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations. Zbl 1007.35040Souplet, Philippe 12 2002 Stability for semilinear parabolic equations with decaying potentials in \(\mathbb{R}^n\) and dynamical approach to the existence of ground states. Zbl 1017.35033Souplet, Philippe; Zhang, Qi S. 11 2002 A priori and universal estimates for global solutions of superlinear degenerate parabolic equations. Zbl 1072.35099Souplet, Philippe 5 2002 Global existence from single-component \(L_{p}\) estimates in a semilinear reaction-diffusion system. Zbl 0993.35048Quittner, Pavol; Souplet, Philippe 3 2002 Recent results and open problems on parabolic equations with gradient nonlinearities. Zbl 0982.35054Souplet, Philippe 37 2001 Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103Fila, Marek; Souplet, Philippe 29 2001 Linear and nonlinear heat equations in \(L^q_\delta\) spaces and universal bounds for global solutions. Zbl 0993.35023Fila, Marek; Souplet, Philippe; Weissler, Fred B. 29 2001 Decay of global solutions, stability and blow up for a reaction-diffusion problem with free boundary. Zbl 0959.35087Ghidouche, Hamid; Souplet, Philippe; Tarzia, Domingo 27 2001 The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046Fila, Marek; Souplet, Philippe 26 2001 Admissible \(L_p\) norms for local existence and for continuation in semilinear parabolic systems are not the same. Zbl 1006.35048Quittner, Pavol; Souplet, Philippe 15 2001 Blowup rates for nonlinear heat equations with gradient terms and for parabolic inequalities. Zbl 0984.35077Souplet, Philippe; Tayachi, Slim 15 2001 Existence of ground states for semilinear elliptic equations with decaying mass: A parabolic approach. Zbl 0992.35029Souplet, Philippe; Zhang, Qi S. 1 2001 Decay of heat semigroups in \(L^\infty\) and applications to nonlinear parabolic problems in unbounded domains. Zbl 0954.35032Souplet, Philippe 11 2000 Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079Martel, Yvan; Souplet, Philippe 7 2000 Blow-up behavior in nonlocal vs. local heat equations. Zbl 0954.35091Souplet, Philippe 1 2000 Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source. Zbl 0923.35077Souplet, Philippe 157 1999 Poincaré’s inequality and global solutions of a nonlinear parabolic equation. Zbl 0924.35065Souplet, Philippe; Weissler, Fred B. 18 1999 Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations. Zbl 0926.35064Souplet, Philippe 16 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 0938.35068Ben-Artzi, Matania; Souplet, Philippe; Weissler, Fred B. 12 1999 Sharp stability estimates for quasi-autonomous evolution equations of hyperbolic type. Zbl 1031.34059Souplet, Philippe 1 1999 Blow-up in nonlocal reaction-diffusion equations. Zbl 0909.35073Souplet, Philippe 164 1998 Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations. Zbl 0892.35078Souplet, Philippe 19 1998 ...and 14 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,803 Authors 58 Winkler, Michael 56 Souplet, Philippe 48 Mu, Chunlai 32 Zheng, Sining 31 Liu, Bingchen 28 Li, Fengjie 25 Ishige, Kazuhiro 22 Fang, Zhongbo 22 Wei, Juncheng 19 Zhang, Zhengce 18 Laurençot, Philippe 18 Quittner, Pavol 17 Ding, Juntang 17 Xiang, Zhaoyin 16 Fujishima, Yohei 16 Zhou, Jun 15 Iagar, Razvan Gabriel 15 Kawakami, Tatsuki 15 Lankeit, Johannes 15 Weissler, Fred B. 15 Xie, Chunhong 14 Li, Yuxiang 14 Wang, Liangchen 14 Zou, Wenming 13 Mizoguchi, Noriko 13 Quaas, Alexander 13 Yanagida, Eiji 13 Zheng, Pan 12 Duong, Anh Tuan 12 Guo, Zongming 12 Jin, Haiyang 12 Lin, Zhigui 12 Wang, Mingxin 12 Zaag, Hatem 11 Fila, Marek 11 García-Melián, Jorge 11 Harrabi, Abdellaziz 11 Liu, Qilin 11 Phan, Quoc Hung 10 Ghergu, Marius 10 Karch, Grzegorz 10 Tayachi, Slim 10 Villavert, John 10 Wang, Wei 10 Wang, Yulan 10 Yang, Zuodong 9 Biler, Piotr 9 Del Pino, Manuel A. 9 Gao, Wenjie 9 Liu, Dengming 9 Ma, Li 9 Poláčik, Peter 9 Taliaferro, Steven D. 9 Tang, Bao Quoc 9 Tao, Youshan 9 Wan, FangShu 9 Weth, Tobias 9 Yin, Jingxue 8 Bidaut-Veron, Marie-Françoise 8 Dai, Wei 8 Deng, Weibing 8 Du, Lili 8 Fellner, Klemens 8 Guo, Jong-Shenq 8 Kirane, Mokhtar 8 Kong, Linghua 8 Lei, Yutian 8 Musso, Monica 8 Parshad, Rana D. 8 Sánchez, Ariel 8 Sierżȩga, Mikołaj 8 Sirakov, Boyan Slavchev 8 Song, Xianfa 8 Stinner, Christian 8 Takahashi, Jin 8 Yang, Hui 8 Yokota, Tomomi 7 Abdellaoui, Boumediene 7 Ahmad, Bashir 7 Chen, Caisheng 7 Chen, Youpeng 7 Chen, Yuqing 7 Ferreira, Raúl 7 Harada, Junichi 7 Kostić, Marko 7 Latos, Evangelos Antonios 7 Liu, Baiyu 7 Liu, Bin 7 Loayza, Miguel 7 Nguyễn Thạc Dũng 7 Punzo, Fabio 7 Rahal, Belgacem 7 Rodríguez-Bernal, Aníbal 7 Samet, Bessem 7 Vernier-Piro, Stella 7 Wang, Xiaoliu 7 Wu, Jiayong 7 Yu, Xiaohui 6 Abolarinwa, Abimbola 6 Al-saedi, Ahmed Eid Salem ...and 1,703 more Authors all top 5 Cited in 251 Serials 174 Journal of Differential Equations 160 Nonlinear Analysis. 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