Edit Profile (opens in new tab) Fila, Marek Compute Distance To: Compute Author ID: fila.marek Published as: Fila, Marek; Fila, M. Homepage: http://www.iam.fmph.uniba.sk/institute/fila/ External Links: MGP Documents Indexed: 109 Publications since 1984 Reviewing Activity: 233 Reviews Co-Authors: 39 Co-Authors with 98 Joint Publications 1,253 Co-Co-Authors all top 5 Co-Authors 11 single-authored 22 Winkler, Michael 14 Yanagida, Eiji 10 Ishige, Kazuhiro 10 Kawakami, Tatsuki 8 Quittner, Pavol 7 Filo, Ján 7 Levine, Howard Allen 6 Chlebík, Miroslav 6 King, John Robert 6 Matano, Hiroshi 6 Poláčik, Peter 4 Kawohl, Bernd 4 Lankeit, Johannes 4 Vazquez, Juan Luis 3 Chipot, Michel 3 Souplet, Philippe 2 Guo, Jong-Shenq 2 Hulshof, Josephus 2 Lieberman, Gary M. 2 Ninomiya, Hirokazu 2 Pulkkinen, Aappo 2 Shafrir, Itai 2 Stuke, Hannes 2 Takahashi, Jin 1 Amann, Herbert 1 Angenent, Sigurd Bernardus 1 Budáč, Ondrej 1 Chen, Xinfu 1 Deng, Keng 1 Macková, Petra 1 Marko, František 1 Mizoguchi, Noriko 1 Raugel, Geneviève 1 Reichel, Wolfgang 1 Sacks, Paul E. 1 Taskinen, Jari 1 Uda, Yoshitaka 1 Velázquez, Juan J. L. 1 Weissler, Fred B. all top 5 Serials 5 Journal of Mathematical Analysis and Applications 5 Advances in Differential Equations 4 Mathematical Methods in the Applied Sciences 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Differential and Integral Equations 4 Discrete and Continuous Dynamical Systems 3 Journal of Differential Equations 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 3 Asymptotic Analysis 3 Acta Mathematica Universitatis Comenianae. New Series 3 Journal of Dynamics and Differential Equations 3 Communications on Pure and Applied Analysis 2 Commentationes Mathematicae Universitatis Carolinae 2 Journal of the London Mathematical Society. Second Series 2 Mathematica Slovaca 2 Tôhoku Mathematical Journal. Second Series 2 Acta Mathematica Universitatis Comenianae 2 Applied Mathematics Letters 2 Advances in Mathematical Sciences and Applications 2 Calculus of Variations and Partial Differential Equations 2 NoDEA. Nonlinear Differential Equations and Applications 2 Nonlinear Analysis. Theory, Methods & Applications 2 Journal of Elliptic and Parabolic Equations 1 Archive for Rational Mechanics and Analysis 1 Israel Journal of Mathematics 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Advances in Mathematics 1 Časopis Pro Pěstování Matematiky 1 Czechoslovak Mathematical Journal 1 Mathematische Zeitschrift 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Quarterly of Applied Mathematics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Journal of Mathematical Sciences. University of Tokyo 1 Revista Matemática Complutense 1 Interfaces and Free Boundaries 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Contemporary Mathematics 1 Nonlinear Boundary Value Problems 1 Journal of Evolution Equations 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S 1 Advances in Nonlinear Analysis all top 5 Fields 107 Partial differential equations (35-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Operator theory (47-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 94 Publications have been cited 1,175 times in 662 Documents Cited by ▼ Year ▼ Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Zbl 0743.35038Chipot, M.; Fila, M.; Quittner, P. 57 1991 The blow-up rate for the heat equation with a nonlinear boundary condition. Zbl 0735.35014Fila, Marek; Quittner, Pavol 46 1991 Existence of positive solutions of a semilinear elliptic equation in \(\mathbb{R}_+^n\) with a nonlinear boundary condition. Zbl 0932.35086Chipot, M.; Chlebík, M.; Fila, M.; Shafrir, I. 42 1998 On the solutions to some elliptic equations with nonlinear Neumann boundary conditions. Zbl 0839.35042Chipot, M.; Shafrir, I.; Fila, M. 41 1996 From critical exponents to blow-up rates for parabolic problems. Zbl 0980.35057Chlebík, M.; Fila, M. 40 1999 On critical exponents for a system of heat equations coupled in the boundary conditions. Zbl 0824.35048Deng, K.; Fila, M.; Levine, H. A. 39 1994 Boundedness of global solutions of nonlinear diffusion equations. Zbl 0764.35010Fila, Marek 31 1992 Derivative blow-up and beyond for quasilinear parabolic equations. Zbl 0811.35059Fila, Marek; Lieberman, Gary M. 30 1994 Quenching on the boundary. Zbl 0809.35043Fila, Marek; Levine, Howard A. 29 1993 The blow-up rate for a semilinear parabolic system. Zbl 0934.35062Fila, Marek; Quittner, Pavol 28 1999 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. 28 2001 Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103Fila, Marek; Souplet, Philippe 27 2001 Blow-up on the boundary: A survey. Zbl 0858.35065Fila, Marek; Filo, Ján 26 1996 Remarks on blow up for a nonlinear parabolic equation with a gradient term. Zbl 0768.35047Fila, Marek 26 1991 A Fujita-type theorem for the Laplace equation with a dynamical boundary condition. Zbl 0922.35053Amann, H.; Fila, M. 24 1997 The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046Fila, Marek; Souplet, Philippe 24 2001 Convergence rate for a parabolic equation with supercritical nonlinearity. Zbl 1087.35049Fila, Marek; Winkler, Michael; Yanagida, Eiji 20 2005 A note on the quenching rate. Zbl 0727.35007Fila, Marek; Hulshof, Josephus 19 1991 Boundedness of global solutions for the heat equation with nonlinear boundary conditions. Zbl 0702.35141Fila, Marek 19 1989 Grow up rate of solutions for a supercritical semilinear diffusion equation. Zbl 1072.35042Fila, Marek; Winkler, Michael; Yanagida, Eiji 18 2004 On critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition. Zbl 0870.35049Fila, Marek; Levine, Howard A. 18 1996 Optimal lower bound of the grow-up rate for a supercritical parabolic equation. Zbl 1102.35017Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 18 2006 Blow-up of positive solutions of a semilinear parabolic equation with a gradient term. Zbl 1028.35071Chlebík, Miroslav; Fila, Marek; Quittner, Pavol 17 2003 Interior gradient blow-up in a semilinear parabolic equation. Zbl 0864.35052Angenent, Sigurd B.; Fila, Marek 17 1996 Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition. Zbl 1279.47092Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 17 2012 Rate of convergence to Barenblatt profiles for the fast diffusion equation. Zbl 1315.76032Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji 17 2012 Immediate regularization after blow-up. Zbl 1102.35053Fila, Marek; Matano, Hiroshi; Polácik, Peter 16 2005 Global solutions of the Laplace equation with a nonlinear dynamical boundary condition. Zbl 0880.35056Fila, Marek; Quittner, Pavol 14 1997 On the blow-up rate for the heat equation with a nonlinear boundary condition. Zbl 0980.35073Chlebík, Miroslav; Fila, Marek 14 2000 Blow-up in nonlinear heat equations from the dynamical systems point of view. Zbl 1004.35060Fila, Marek; Matano, Hiroshi 14 2002 Large time behavior of solutions of a semilinear parabolic equation with a nonlinear dynamical boundary condition. Zbl 0935.35072Fila, Marek; Quittner, Pavol 14 1999 Quenching for quasilinear equations. Zbl 0801.35057Fila, Marek; Kawohl, Bernhard; Levine, Howard A. 14 1992 Asymptotic analysis of quenching problems. Zbl 0798.35079Fila, Marek; Kawohl, Bernhard 13 1992 Complete blow-up and incomplete quenching for the heat equation with a nonlinear boundary condition. Zbl 0994.35066Fila, Marek; Guo, Jong-Shenq 13 2002 Reaction versus diffusion: Blow-up induced and inhibited by diffusivity. Zbl 1171.35411Fila, M.; Ninomiya, H. 12 2005 Some recent results on blow-up on the boundary for the heat equation. Zbl 0969.35080Chlebík, Miroslav; Fila, Marek 12 2000 Boundedness of global solutions of a supercritical parabolic equation. Zbl 1128.35057Chen, Xinfu; Fila, Marek; Guo, Jong-Shenq 12 2008 Stabilization of solutions of weakly singular quenching problems. Zbl 0785.35054Fila, Marek; Levine, Howard A.; Vazquez, Juan L. 12 1993 Large time behavior of solutions to a quasilinear parabolic equation with a nonlinear boundary condition. Zbl 1194.35055Fila, Marek; Kawohl, Bernd 11 2001 The quenching problem on the \(N\)-dimensional ball. Zbl 0792.35097Fila, Marek; Hulshof, Josephus; Quittner, Pavol 11 1992 Multiple continuation beyond blow-up. Zbl 1212.35231Fila, Marek; Mizoguchi, Noriko 10 2007 Blow-up of solutions of supercritical parabolic equations. Zbl 1093.35042Fila, Marek 9 2005 Convergence to a singular steady state of a parabolic equation with gradient blow-up. Zbl 1125.35367Fila, Marek; Taskinen, Jari; Winkler, Michael 9 2007 Slow convergence to zero for a parabolic equation with a supercritical nonlinearity. Zbl 1263.35138Fila, Marek; Winkler, Michael; Yanagida, Eiji 9 2008 A continuum of extinction rates for the fast diffusion equation. Zbl 1229.35124Fila, Marek; Vázquez, Juan-Luis; Winkler, Michael 9 2011 Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems. Zbl 1120.35048Fila, Marek; Ninomiya, Hirokazu; Vázquez, Juan Luis 9 2006 Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1281.35051Fila, M.; Ishige, K.; Kawakami, T. 9 2013 A Fujita-type global existence – global non-existence theorem for a system of reaction diffusion equations with differing diffusivities. Zbl 0814.35046Fila, Marek; Levine, Howard A.; Uda, Yoshitaka 9 1994 Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1329.35156Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 8 2015 Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation. Zbl 1349.35168Fila, Marek; Winkler, Michael 8 2016 Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030Fila, Marek; Poláčik, Peter 8 1999 Blow-up on the boundary for the heat equation. Zbl 0939.35098Fila, Marek; Filo, Ján; Lieberman, Gary M. 8 2000 Is quenching in infinite time possible? Zbl 0737.35005Fila, Marek; Kawohl, Bernhard 8 1990 Homoclinic and heteroclinic orbits for a semilinear parabolic equation. Zbl 1252.35157Fila, Marek; Yanagida, Eiji 8 2011 Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent. Zbl 1295.35085Fila, M.; King, J. R.; Winkler, M. 7 2014 Convergence to self-similar solutions for a semilinear parabolic equation. Zbl 1155.35005Fila, Marek; Winkler, Michael; Yanagida, Eiji 7 2008 Rate of convergence to a singular steady state of a supercritical parabolic equation. Zbl 1175.35071Fila, Marek; Winkler, Michael 7 2008 Nonconstant selfsimilar blow-up profile for the exponential reaction-diffusion equation. Zbl 1158.35056Fila, Marek; Pulkkinen, Aappo 7 2008 Global solutions of a semilinear parabolic equation. Zbl 0953.35065Fila, Marek; Poláčik, Peter 6 1999 Large-time behavior of small solutions of a two-dimensional semilinear elliptic equation with a dynamical boundary condition. Zbl 1280.35051Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 6 2013 On the boundedness of global solutions of abstract semilinear parabolic equations. Zbl 0892.35069Fila, Marek; Levine, Howard A. 6 1997 Rate of convergence to separable solutions of the fast diffusion equation. Zbl 1348.35120Fila, Marek; Winkler, Michael 6 2016 Linear behaviour of solutions of a superlinear heat equation. Zbl 1263.35137Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 6 2008 Radial positive solutions for a semilinear elliptic equation with a gradient term. Zbl 0803.35035Fila, M.; Quittner, P. 6 1993 Grow up and slow decay in the critical Sobolev case. Zbl 1262.35032Fila, Marek; King, John R. 6 2012 Slow growth of solutions of superfast diffusion equations with unbounded initial data. Zbl 1386.35178Fila, Marek; Winkler, Michael 6 2017 Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054Fila, Marek; Matano, Hiroshi; Poláčik, Peter 5 2002 Boundedness of global solutions of nonlocal parabolic equations. Zbl 0902.35055Fila, Marek 5 1997 Backward selfsimilar solutions of supercritical parabolic equations. Zbl 1173.35547Fila, Marek; Pulkkinen, Aappo 5 2009 Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1344.35055Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 4 2016 Connecting equilibria by blow-up solutions. Zbl 1157.35404Fila, Marek; Matano, Hiroshi 4 2000 Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition. Zbl 1433.35395Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki; Lankeit, Johannes 4 2019 Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent. Zbl 1170.35456Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 4 2007 Lack of smoothing for bounded solutions of a semilinear parabolic equation. Zbl 1436.35243Fila, Marek; Lankeit, Johannes 4 2020 An exterior nonlinear elliptic problem with a dynamical boundary condition. Zbl 1377.35111Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 4 2017 Grow-up on the boundary for a semilinear parabolic problem. Zbl 1090.35034Fila, Marek; Velázquez, Juan J. L.; Winkler, Michael 3 2005 Special asymptotics for a critical fast diffusion equation. Zbl 1284.35239Fila, Marek; Stuke, Hannes 3 2014 Very slow grow-up of solutions of a semi-linear parabolic equation. Zbl 1221.35064Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 3 2011 A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation. Zbl 1428.26026Fila, Marek; Winkler, Michael 3 2019 Solutions with moving singularities for equations of porous medium type. Zbl 1404.35270Fila, Marek; Takahashi, Jin; Yanagida, Eiji 3 2019 Immediate regularization after blow-up. Zbl 1108.35092Fila, M.; Matano, H.; Poláčik, P. 3 2005 A blow-up result for nonlinear diffusion equations. Zbl 0704.35071Fila, Marek; Filo, Ján 2 1989 Stabilization of solutions of certain one-dimensional degenerate diffusion equations. Zbl 0619.35064Fila, Marek; Filo, Ján 2 1987 Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed. Zbl 1190.35038Fila, Marek; Winkler, Michael 2 2008 Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition. Zbl 1274.35136Chlebík, Miroslav; Fila, Marek; Reichel, Wolfgang 2 2003 Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation. Zbl 1321.35102Fila, Marek; Winkler, Michael 2 2015 Non-accessible singular homoclinic orbits for a semilinear parabolic equation. Zbl 1340.35179Fila, Marek; Yanagida, Eiji 2 2014 Convergence of solutions of a semilinear parabolic equation to selfsimilar solutions of the linear heat equation. Zbl 1178.35068Fila, Marek; Winkler, Michael; Yanagida, Eiji 2 2008 The transition from decay to blow-up in some reaction-diffusion-convection equations. Zbl 0849.35057Fila, Marek; Sacks, Paul 2 1996 Blow up for a nonlinear degenerate parabolic equation. Zbl 0729.35017Fila, M.; Filo, J. 1 1990 Boundedness of global solutions of nonlinear parabolic equations. Zbl 1046.35009Fila, Marek 1 2002 Continuation beyond interior gradient blow-up in a semilinear parabolic equation. Zbl 1448.35309Fila, Marek; Lankeit, Johannes 1 2020 The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition. Zbl 1446.35046Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki; Lankeit, Johannes 1 2020 The large diffusion limit for the heat equation with a dynamical boundary condition. Zbl 1450.35031Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 1 2021 The large diffusion limit for the heat equation with a dynamical boundary condition. Zbl 1450.35031Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 1 2021 Lack of smoothing for bounded solutions of a semilinear parabolic equation. Zbl 1436.35243Fila, Marek; Lankeit, Johannes 4 2020 Continuation beyond interior gradient blow-up in a semilinear parabolic equation. Zbl 1448.35309Fila, Marek; Lankeit, Johannes 1 2020 The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition. Zbl 1446.35046Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki; Lankeit, Johannes 1 2020 Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition. Zbl 1433.35395Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki; Lankeit, Johannes 4 2019 A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation. Zbl 1428.26026Fila, Marek; Winkler, Michael 3 2019 Solutions with moving singularities for equations of porous medium type. Zbl 1404.35270Fila, Marek; Takahashi, Jin; Yanagida, Eiji 3 2019 Slow growth of solutions of superfast diffusion equations with unbounded initial data. Zbl 1386.35178Fila, Marek; Winkler, Michael 6 2017 An exterior nonlinear elliptic problem with a dynamical boundary condition. Zbl 1377.35111Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 4 2017 Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation. Zbl 1349.35168Fila, Marek; Winkler, Michael 8 2016 Rate of convergence to separable solutions of the fast diffusion equation. Zbl 1348.35120Fila, Marek; Winkler, Michael 6 2016 Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1344.35055Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 4 2016 Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1329.35156Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 8 2015 Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation. Zbl 1321.35102Fila, Marek; Winkler, Michael 2 2015 Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent. Zbl 1295.35085Fila, M.; King, J. R.; Winkler, M. 7 2014 Special asymptotics for a critical fast diffusion equation. Zbl 1284.35239Fila, Marek; Stuke, Hannes 3 2014 Non-accessible singular homoclinic orbits for a semilinear parabolic equation. Zbl 1340.35179Fila, Marek; Yanagida, Eiji 2 2014 Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1281.35051Fila, M.; Ishige, K.; Kawakami, T. 9 2013 Large-time behavior of small solutions of a two-dimensional semilinear elliptic equation with a dynamical boundary condition. Zbl 1280.35051Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 6 2013 Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition. Zbl 1279.47092Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki 17 2012 Rate of convergence to Barenblatt profiles for the fast diffusion equation. Zbl 1315.76032Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji 17 2012 Grow up and slow decay in the critical Sobolev case. Zbl 1262.35032Fila, Marek; King, John R. 6 2012 A continuum of extinction rates for the fast diffusion equation. Zbl 1229.35124Fila, Marek; Vázquez, Juan-Luis; Winkler, Michael 9 2011 Homoclinic and heteroclinic orbits for a semilinear parabolic equation. Zbl 1252.35157Fila, Marek; Yanagida, Eiji 8 2011 Very slow grow-up of solutions of a semi-linear parabolic equation. Zbl 1221.35064Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 3 2011 Backward selfsimilar solutions of supercritical parabolic equations. Zbl 1173.35547Fila, Marek; Pulkkinen, Aappo 5 2009 Boundedness of global solutions of a supercritical parabolic equation. Zbl 1128.35057Chen, Xinfu; Fila, Marek; Guo, Jong-Shenq 12 2008 Slow convergence to zero for a parabolic equation with a supercritical nonlinearity. Zbl 1263.35138Fila, Marek; Winkler, Michael; Yanagida, Eiji 9 2008 Convergence to self-similar solutions for a semilinear parabolic equation. Zbl 1155.35005Fila, Marek; Winkler, Michael; Yanagida, Eiji 7 2008 Rate of convergence to a singular steady state of a supercritical parabolic equation. Zbl 1175.35071Fila, Marek; Winkler, Michael 7 2008 Nonconstant selfsimilar blow-up profile for the exponential reaction-diffusion equation. Zbl 1158.35056Fila, Marek; Pulkkinen, Aappo 7 2008 Linear behaviour of solutions of a superlinear heat equation. Zbl 1263.35137Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 6 2008 Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed. Zbl 1190.35038Fila, Marek; Winkler, Michael 2 2008 Convergence of solutions of a semilinear parabolic equation to selfsimilar solutions of the linear heat equation. Zbl 1178.35068Fila, Marek; Winkler, Michael; Yanagida, Eiji 2 2008 Multiple continuation beyond blow-up. Zbl 1212.35231Fila, Marek; Mizoguchi, Noriko 10 2007 Convergence to a singular steady state of a parabolic equation with gradient blow-up. Zbl 1125.35367Fila, Marek; Taskinen, Jari; Winkler, Michael 9 2007 Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent. Zbl 1170.35456Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 4 2007 Optimal lower bound of the grow-up rate for a supercritical parabolic equation. Zbl 1102.35017Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 18 2006 Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems. Zbl 1120.35048Fila, Marek; Ninomiya, Hirokazu; Vázquez, Juan Luis 9 2006 Convergence rate for a parabolic equation with supercritical nonlinearity. Zbl 1087.35049Fila, Marek; Winkler, Michael; Yanagida, Eiji 20 2005 Immediate regularization after blow-up. Zbl 1102.35053Fila, Marek; Matano, Hiroshi; Polácik, Peter 16 2005 Reaction versus diffusion: Blow-up induced and inhibited by diffusivity. Zbl 1171.35411Fila, M.; Ninomiya, H. 12 2005 Blow-up of solutions of supercritical parabolic equations. Zbl 1093.35042Fila, Marek 9 2005 Grow-up on the boundary for a semilinear parabolic problem. Zbl 1090.35034Fila, Marek; Velázquez, Juan J. L.; Winkler, Michael 3 2005 Immediate regularization after blow-up. Zbl 1108.35092Fila, M.; Matano, H.; Poláčik, P. 3 2005 Grow up rate of solutions for a supercritical semilinear diffusion equation. Zbl 1072.35042Fila, Marek; Winkler, Michael; Yanagida, Eiji 18 2004 Blow-up of positive solutions of a semilinear parabolic equation with a gradient term. Zbl 1028.35071Chlebík, Miroslav; Fila, Marek; Quittner, Pavol 17 2003 Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition. Zbl 1274.35136Chlebík, Miroslav; Fila, Marek; Reichel, Wolfgang 2 2003 Blow-up in nonlinear heat equations from the dynamical systems point of view. Zbl 1004.35060Fila, Marek; Matano, Hiroshi 14 2002 Complete blow-up and incomplete quenching for the heat equation with a nonlinear boundary condition. Zbl 0994.35066Fila, Marek; Guo, Jong-Shenq 13 2002 Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054Fila, Marek; Matano, Hiroshi; Poláčik, Peter 5 2002 Boundedness of global solutions of nonlinear parabolic equations. Zbl 1046.35009Fila, Marek 1 2002 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. 28 2001 Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103Fila, Marek; Souplet, Philippe 27 2001 The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046Fila, Marek; Souplet, Philippe 24 2001 Large time behavior of solutions to a quasilinear parabolic equation with a nonlinear boundary condition. Zbl 1194.35055Fila, Marek; Kawohl, Bernd 11 2001 On the blow-up rate for the heat equation with a nonlinear boundary condition. Zbl 0980.35073Chlebík, Miroslav; Fila, Marek 14 2000 Some recent results on blow-up on the boundary for the heat equation. Zbl 0969.35080Chlebík, Miroslav; Fila, Marek 12 2000 Blow-up on the boundary for the heat equation. Zbl 0939.35098Fila, Marek; Filo, Ján; Lieberman, Gary M. 8 2000 Connecting equilibria by blow-up solutions. Zbl 1157.35404Fila, Marek; Matano, Hiroshi 4 2000 From critical exponents to blow-up rates for parabolic problems. Zbl 0980.35057Chlebík, M.; Fila, M. 40 1999 The blow-up rate for a semilinear parabolic system. Zbl 0934.35062Fila, Marek; Quittner, Pavol 28 1999 Large time behavior of solutions of a semilinear parabolic equation with a nonlinear dynamical boundary condition. Zbl 0935.35072Fila, Marek; Quittner, Pavol 14 1999 Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030Fila, Marek; Poláčik, Peter 8 1999 Global solutions of a semilinear parabolic equation. Zbl 0953.35065Fila, Marek; Poláčik, Peter 6 1999 Existence of positive solutions of a semilinear elliptic equation in \(\mathbb{R}_+^n\) with a nonlinear boundary condition. Zbl 0932.35086Chipot, M.; Chlebík, M.; Fila, M.; Shafrir, I. 42 1998 A Fujita-type theorem for the Laplace equation with a dynamical boundary condition. Zbl 0922.35053Amann, H.; Fila, M. 24 1997 Global solutions of the Laplace equation with a nonlinear dynamical boundary condition. Zbl 0880.35056Fila, Marek; Quittner, Pavol 14 1997 On the boundedness of global solutions of abstract semilinear parabolic equations. Zbl 0892.35069Fila, Marek; Levine, Howard A. 6 1997 Boundedness of global solutions of nonlocal parabolic equations. Zbl 0902.35055Fila, Marek 5 1997 On the solutions to some elliptic equations with nonlinear Neumann boundary conditions. Zbl 0839.35042Chipot, M.; Shafrir, I.; Fila, M. 41 1996 Blow-up on the boundary: A survey. Zbl 0858.35065Fila, Marek; Filo, Ján 26 1996 On critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition. Zbl 0870.35049Fila, Marek; Levine, Howard A. 18 1996 Interior gradient blow-up in a semilinear parabolic equation. Zbl 0864.35052Angenent, Sigurd B.; Fila, Marek 17 1996 The transition from decay to blow-up in some reaction-diffusion-convection equations. Zbl 0849.35057Fila, Marek; Sacks, Paul 2 1996 On critical exponents for a system of heat equations coupled in the boundary conditions. Zbl 0824.35048Deng, K.; Fila, M.; Levine, H. A. 39 1994 Derivative blow-up and beyond for quasilinear parabolic equations. Zbl 0811.35059Fila, Marek; Lieberman, Gary M. 30 1994 A Fujita-type global existence – global non-existence theorem for a system of reaction diffusion equations with differing diffusivities. Zbl 0814.35046Fila, Marek; Levine, Howard A.; Uda, Yoshitaka 9 1994 Quenching on the boundary. Zbl 0809.35043Fila, Marek; Levine, Howard A. 29 1993 Stabilization of solutions of weakly singular quenching problems. Zbl 0785.35054Fila, Marek; Levine, Howard A.; Vazquez, Juan L. 12 1993 Radial positive solutions for a semilinear elliptic equation with a gradient term. Zbl 0803.35035Fila, M.; Quittner, P. 6 1993 Boundedness of global solutions of nonlinear diffusion equations. Zbl 0764.35010Fila, Marek 31 1992 Quenching for quasilinear equations. Zbl 0801.35057Fila, Marek; Kawohl, Bernhard; Levine, Howard A. 14 1992 Asymptotic analysis of quenching problems. Zbl 0798.35079Fila, Marek; Kawohl, Bernhard 13 1992 The quenching problem on the \(N\)-dimensional ball. Zbl 0792.35097Fila, Marek; Hulshof, Josephus; Quittner, Pavol 11 1992 Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Zbl 0743.35038Chipot, M.; Fila, M.; Quittner, P. 57 1991 The blow-up rate for the heat equation with a nonlinear boundary condition. Zbl 0735.35014Fila, Marek; Quittner, Pavol 46 1991 Remarks on blow up for a nonlinear parabolic equation with a gradient term. Zbl 0768.35047Fila, Marek 26 1991 A note on the quenching rate. Zbl 0727.35007Fila, Marek; Hulshof, Josephus 19 1991 Is quenching in infinite time possible? Zbl 0737.35005Fila, Marek; Kawohl, Bernhard 8 1990 Blow up for a nonlinear degenerate parabolic equation. Zbl 0729.35017Fila, M.; Filo, J. 1 1990 Boundedness of global solutions for the heat equation with nonlinear boundary conditions. Zbl 0702.35141Fila, Marek 19 1989 A blow-up result for nonlinear diffusion equations. Zbl 0704.35071Fila, Marek; Filo, Ján 2 1989 Stabilization of solutions of certain one-dimensional degenerate diffusion equations. Zbl 0619.35064Fila, Marek; Filo, Ján 2 1987 all cited Publications top 5 cited Publications all top 5 Cited by 671 Authors 40 Fila, Marek 32 Souplet, Philippe 24 Winkler, Michael 23 Rossi, Julio Daniel 22 Zheng, Sining 20 Ishige, Kazuhiro 16 Kawakami, Tatsuki 16 Wang, Mingxin 15 Lin, Zhigui 15 Yanagida, Eiji 14 Quittner, Pavol 13 Li, Fengjie 13 Liu, Bingchen 13 Mu, Chunlai 10 Quirós Gracián, Fernando 9 Ferreira, Raúl 9 Guo, Jong-Shenq 9 Xie, Chunhong 8 Mizoguchi, Noriko 8 Song, Xianfa 8 Vazquez, Juan Luis 7 de Pablo, Arturo 7 Fujishima, Yohei 7 Hu, Bei 7 Ji, Ruihong 7 Kirane, Mokhtar 7 Levine, Howard Allen 7 Zhang, Zhengce 6 Deng, Keng 6 Harada, Junichi 6 Poláčik, Peter 6 Wang, Shu 6 Wei, Juncheng 6 Yin, Jingxue 6 Zaag, Hatem 5 Dratman, Ezequiel 5 Hui, Kin Ming 5 Lankeit, Johannes 5 Punzo, Fabio 5 Rodríguez-Bernal, Aníbal 5 Wang, Wei 5 Xing, Ruixiang 5 Yin, Hongming 5 Zhou, Mingjun 4 Brändle, Cristina 4 Chen, Shaohua 4 Dávila, Juan 4 Ding, Juntang 4 Fernández Bonder, Julián 4 Filo, Ján 4 Ghoul, Tej-Eddine 4 Hong, Li 4 King, John Robert 4 Korpusov, Maksim Olegovich 4 Li, Huiling 4 Matera, Guillermo 4 Meglioli, Giulia 4 da Silva Montenegro, Marcelo 4 Naito, Yūki 4 Nguyen, Van Tien 4 Sierżȩga, Mikołaj 4 Takahashi, Jin 4 Tan, Jinggang 4 Tan, Zhong 4 Umezu, Kenichiro 4 Vulkov, Lubin G. 4 Wang, Weimin 4 Wang, Zejia 4 Weissler, Fred B. 4 Zheng, Gao-Feng 4 Zhou, Peng 3 Ahmad, Bashir 3 Al-saedi, Ahmed Eid Salem 3 Andreu, Fuensanta 3 Arrieta, José M. 3 Charkaoui, Abderrahim 3 Chipot, Michel 3 Diaz Diaz, Jesus Ildefonso 3 Eddine Alaa, Nour 3 Fang, Zhongbo 3 Ferreira, Lucas Catão de Freitas 3 Furtado, Marcelo Fernandes 3 Galaktionov, Victor Aleksandrovich 3 Grillo, Gabriele 3 Hamamuki, Nao 3 Hoshino, Masaki 3 Jiang, Zhaoxin 3 Kavallaris, Nikos I. 3 Kim, Kwang Ik 3 Li, Xiaojun 3 Li, YanYan 3 Ling, Zhi 3 Liu, Qilin 3 Mahmoudi, Nejib 3 Matsue, Kaname 3 Merle, Frank 3 Okamoto, Hisashi 3 Pan, Hongjing 3 Parshad, Rana D. 3 Pérez-Llanos, Mayte ...and 571 more Authors all top 5 Cited in 148 Serials 64 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 63 Journal of Mathematical Analysis and Applications 57 Journal of Differential Equations 21 Applied Mathematics and Computation 20 Applied Mathematics Letters 17 Discrete and Continuous Dynamical Systems 15 Journal of Functional Analysis 15 Calculus of Variations and Partial Differential Equations 12 Applicable Analysis 12 Mathematische Annalen 10 Mathematical Methods in the Applied Sciences 10 Proceedings of the American Mathematical Society 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 Computers & Mathematics with Applications 9 Nonlinear Analysis. Real World Applications 9 Boundary Value Problems 9 SN Partial Differential Equations and Applications 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Acta Mathematica Sinica. English Series 8 Nonlinear Analysis. Theory, Methods & Applications 7 Journal of Computational and Applied Mathematics 7 Quarterly of Applied Mathematics 7 Transactions of the American Mathematical Society 6 Archive for Rational Mechanics and Analysis 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 SIAM Journal on Mathematical Analysis 6 Journal of Dynamics and Differential Equations 6 NoDEA. Nonlinear Differential Equations and Applications 6 Differential Equations 5 Rocky Mountain Journal of Mathematics 5 Communications in Partial Differential Equations 5 Journal of Evolution Equations 5 Communications on Pure and Applied Analysis 4 Israel Journal of Mathematics 4 Mathematical Notes 4 Advances in Mathematics 4 Duke Mathematical Journal 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Applied Mathematics. Series B (English Edition) 4 Communications in Contemporary Mathematics 4 Discrete and Continuous Dynamical Systems. Series B 4 Advances in Nonlinear Analysis 3 Journal d’Analyse Mathématique 3 Nonlinearity 3 Czechoslovak Mathematical Journal 3 Numerische Mathematik 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Tôhoku Mathematical Journal. Second Series 3 Zeitschrift für Analysis und ihre Anwendungen 3 Science in China. Series A 3 Journal of Inequalities and Applications 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Discrete and Continuous Dynamical Systems. Series S 3 Science China. Mathematics 3 Journal of Elliptic and Parabolic Equations 2 Journal of Engineering Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Archiv der Mathematik 2 International Journal of Mathematics and Mathematical Sciences 2 Results in Mathematics 2 Siberian Mathematical Journal 2 Tokyo Journal of Mathematics 2 Physica D 2 Journal of Complexity 2 Mathematical and Computer Modelling 2 Journal of Integral Equations and Applications 2 The Journal of Geometric Analysis 2 Journal of Mathematical Sciences (New York) 2 Electronic Journal of Differential Equations (EJDE) 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Abstract and Applied Analysis 2 Taiwanese Journal of Mathematics 2 Revista Matemática Complutense 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Dynamical and Control Systems 2 Advanced Nonlinear Studies 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Central European Journal of Mathematics 2 TWMS Journal of Pure and Applied Mathematics 2 Electronic Research Archive 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 Journal of Mathematical Biology 1 Lithuanian Mathematical Journal 1 Computing 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Meccanica 1 Michigan Mathematical Journal 1 Osaka Journal of Mathematics 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Theoretical Computer Science 1 Applied Mathematics and Mechanics. (English Edition) ...and 48 more Serials all top 5 Cited in 28 Fields 630 Partial differential equations (35-XX) 38 Numerical analysis (65-XX) 24 Ordinary differential equations (34-XX) 21 Biology and other natural sciences (92-XX) 16 Integral equations (45-XX) 15 Fluid mechanics (76-XX) 12 Differential geometry (53-XX) 12 Global analysis, analysis on manifolds (58-XX) 9 Real functions (26-XX) 9 Operator theory (47-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Mechanics of deformable solids (74-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Functional analysis (46-XX) 5 Difference and functional equations (39-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Optics, electromagnetic theory (78-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Field theory and polynomials (12-XX) 2 Potential theory (31-XX) 2 Systems theory; control (93-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year