## Fila, Marek

Compute Distance To:
 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
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### 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.
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### 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
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### 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)

### 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 0743.35038
Chipot, M.; Fila, M.; Quittner, P.
1991
The blow-up rate for the heat equation with a nonlinear boundary condition. Zbl 0735.35014
Fila, Marek; Quittner, Pavol
1991
Existence of positive solutions of a semilinear elliptic equation in $$\mathbb{R}_+^n$$ with a nonlinear boundary condition. Zbl 0932.35086
Chipot, M.; Chlebík, M.; Fila, M.; Shafrir, I.
1998
On the solutions to some elliptic equations with nonlinear Neumann boundary conditions. Zbl 0839.35042
Chipot, M.; Shafrir, I.; Fila, M.
1996
From critical exponents to blow-up rates for parabolic problems. Zbl 0980.35057
Chlebík, M.; Fila, M.
1999
On critical exponents for a system of heat equations coupled in the boundary conditions. Zbl 0824.35048
Deng, K.; Fila, M.; Levine, H. A.
1994
Boundedness of global solutions of nonlinear diffusion equations. Zbl 0764.35010
Fila, Marek
1992
Derivative blow-up and beyond for quasilinear parabolic equations. Zbl 0811.35059
Fila, Marek; Lieberman, Gary M.
1994
Quenching on the boundary. Zbl 0809.35043
Fila, Marek; Levine, Howard A.
1993
The blow-up rate for a semilinear parabolic system. Zbl 0934.35062
Fila, Marek; Quittner, Pavol
1999
Linear and nonlinear heat equations in $$L^q_\delta$$ spaces and universal bounds for global solutions. Zbl 0993.35023
Fila, Marek; Souplet, Philippe; Weissler, Fred B.
2001
Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103
Fila, Marek; Souplet, Philippe
2001
Blow-up on the boundary: A survey. Zbl 0858.35065
Fila, Marek; Filo, Ján
1996
Remarks on blow up for a nonlinear parabolic equation with a gradient term. Zbl 0768.35047
Fila, Marek
1991
A Fujita-type theorem for the Laplace equation with a dynamical boundary condition. Zbl 0922.35053
Amann, H.; Fila, M.
1997
The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046
Fila, Marek; Souplet, Philippe
2001
Convergence rate for a parabolic equation with supercritical nonlinearity. Zbl 1087.35049
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2005
A note on the quenching rate. Zbl 0727.35007
Fila, Marek; Hulshof, Josephus
1991
Boundedness of global solutions for the heat equation with nonlinear boundary conditions. Zbl 0702.35141
Fila, Marek
1989
Grow up rate of solutions for a supercritical semilinear diffusion equation. Zbl 1072.35042
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2004
On critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition. Zbl 0870.35049
Fila, Marek; Levine, Howard A.
1996
Optimal lower bound of the grow-up rate for a supercritical parabolic equation. Zbl 1102.35017
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2006
Blow-up of positive solutions of a semilinear parabolic equation with a gradient term. Zbl 1028.35071
Chlebík, Miroslav; Fila, Marek; Quittner, Pavol
2003
Interior gradient blow-up in a semilinear parabolic equation. Zbl 0864.35052
Angenent, Sigurd B.; Fila, Marek
1996
Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition. Zbl 1279.47092
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2012
Rate of convergence to Barenblatt profiles for the fast diffusion equation. Zbl 1315.76032
Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji
2012
Immediate regularization after blow-up. Zbl 1102.35053
Fila, Marek; Matano, Hiroshi; Polácik, Peter
2005
Global solutions of the Laplace equation with a nonlinear dynamical boundary condition. Zbl 0880.35056
Fila, Marek; Quittner, Pavol
1997
On the blow-up rate for the heat equation with a nonlinear boundary condition. Zbl 0980.35073
Chlebík, Miroslav; Fila, Marek
2000
Blow-up in nonlinear heat equations from the dynamical systems point of view. Zbl 1004.35060
Fila, Marek; Matano, Hiroshi
2002
Large time behavior of solutions of a semilinear parabolic equation with a nonlinear dynamical boundary condition. Zbl 0935.35072
Fila, Marek; Quittner, Pavol
1999
Quenching for quasilinear equations. Zbl 0801.35057
Fila, Marek; Kawohl, Bernhard; Levine, Howard A.
1992
Asymptotic analysis of quenching problems. Zbl 0798.35079
Fila, Marek; Kawohl, Bernhard
1992
Complete blow-up and incomplete quenching for the heat equation with a nonlinear boundary condition. Zbl 0994.35066
Fila, Marek; Guo, Jong-Shenq
2002
Reaction versus diffusion: Blow-up induced and inhibited by diffusivity. Zbl 1171.35411
Fila, M.; Ninomiya, H.
2005
Some recent results on blow-up on the boundary for the heat equation. Zbl 0969.35080
Chlebík, Miroslav; Fila, Marek
2000
Boundedness of global solutions of a supercritical parabolic equation. Zbl 1128.35057
Chen, Xinfu; Fila, Marek; Guo, Jong-Shenq
2008
Stabilization of solutions of weakly singular quenching problems. Zbl 0785.35054
Fila, Marek; Levine, Howard A.; Vazquez, Juan L.
1993
Large time behavior of solutions to a quasilinear parabolic equation with a nonlinear boundary condition. Zbl 1194.35055
Fila, Marek; Kawohl, Bernd
2001
The quenching problem on the $$N$$-dimensional ball. Zbl 0792.35097
Fila, Marek; Hulshof, Josephus; Quittner, Pavol
1992
Multiple continuation beyond blow-up. Zbl 1212.35231
Fila, Marek; Mizoguchi, Noriko
2007
Blow-up of solutions of supercritical parabolic equations. Zbl 1093.35042
Fila, Marek
2005
Convergence to a singular steady state of a parabolic equation with gradient blow-up. Zbl 1125.35367
Fila, Marek; Taskinen, Jari; Winkler, Michael
2007
Slow convergence to zero for a parabolic equation with a supercritical nonlinearity. Zbl 1263.35138
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2008
A continuum of extinction rates for the fast diffusion equation. Zbl 1229.35124
Fila, Marek; Vázquez, Juan-Luis; Winkler, Michael
2011
Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems. Zbl 1120.35048
Fila, Marek; Ninomiya, Hirokazu; Vázquez, Juan Luis
2006
Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1281.35051
Fila, M.; Ishige, K.; Kawakami, T.
2013
A Fujita-type global existence – global non-existence theorem for a system of reaction diffusion equations with differing diffusivities. Zbl 0814.35046
Fila, Marek; Levine, Howard A.; Uda, Yoshitaka
1994
Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1329.35156
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2015
Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation. Zbl 1349.35168
Fila, Marek; Winkler, Michael
2016
Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030
Fila, Marek; Poláčik, Peter
1999
Blow-up on the boundary for the heat equation. Zbl 0939.35098
Fila, Marek; Filo, Ján; Lieberman, Gary M.
2000
Is quenching in infinite time possible? Zbl 0737.35005
Fila, Marek; Kawohl, Bernhard
1990
Homoclinic and heteroclinic orbits for a semilinear parabolic equation. Zbl 1252.35157
Fila, Marek; Yanagida, Eiji
2011
Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent. Zbl 1295.35085
Fila, M.; King, J. R.; Winkler, M.
2014
Convergence to self-similar solutions for a semilinear parabolic equation. Zbl 1155.35005
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2008
Rate of convergence to a singular steady state of a supercritical parabolic equation. Zbl 1175.35071
Fila, Marek; Winkler, Michael
2008
Nonconstant selfsimilar blow-up profile for the exponential reaction-diffusion equation. Zbl 1158.35056
Fila, Marek; Pulkkinen, Aappo
2008
Global solutions of a semilinear parabolic equation. Zbl 0953.35065
Fila, Marek; Poláčik, Peter
1999
Large-time behavior of small solutions of a two-dimensional semilinear elliptic equation with a dynamical boundary condition. Zbl 1280.35051
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2013
On the boundedness of global solutions of abstract semilinear parabolic equations. Zbl 0892.35069
Fila, Marek; Levine, Howard A.
1997
Rate of convergence to separable solutions of the fast diffusion equation. Zbl 1348.35120
Fila, Marek; Winkler, Michael
2016
Linear behaviour of solutions of a superlinear heat equation. Zbl 1263.35137
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2008
Radial positive solutions for a semilinear elliptic equation with a gradient term. Zbl 0803.35035
Fila, M.; Quittner, P.
1993
Grow up and slow decay in the critical Sobolev case. Zbl 1262.35032
Fila, Marek; King, John R.
2012
Slow growth of solutions of superfast diffusion equations with unbounded initial data. Zbl 1386.35178
Fila, Marek; Winkler, Michael
2017
Existence of $$L^1$$-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054
Fila, Marek; Matano, Hiroshi; Poláčik, Peter
2002
Boundedness of global solutions of nonlocal parabolic equations. Zbl 0902.35055
Fila, Marek
1997
Backward selfsimilar solutions of supercritical parabolic equations. Zbl 1173.35547
Fila, Marek; Pulkkinen, Aappo
2009
Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1344.35055
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2016
Connecting equilibria by blow-up solutions. Zbl 1157.35404
Fila, Marek; Matano, Hiroshi
2000
Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition. Zbl 1433.35395
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki; Lankeit, Johannes
2019
Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent. Zbl 1170.35456
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2007
Lack of smoothing for bounded solutions of a semilinear parabolic equation. Zbl 1436.35243
Fila, Marek; Lankeit, Johannes
2020
An exterior nonlinear elliptic problem with a dynamical boundary condition. Zbl 1377.35111
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2017
Grow-up on the boundary for a semilinear parabolic problem. Zbl 1090.35034
Fila, Marek; Velázquez, Juan J. L.; Winkler, Michael
2005
Special asymptotics for a critical fast diffusion equation. Zbl 1284.35239
Fila, Marek; Stuke, Hannes
2014
Very slow grow-up of solutions of a semi-linear parabolic equation. Zbl 1221.35064
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2011
A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation. Zbl 1428.26026
Fila, Marek; Winkler, Michael
2019
Solutions with moving singularities for equations of porous medium type. Zbl 1404.35270
Fila, Marek; Takahashi, Jin; Yanagida, Eiji
2019
Immediate regularization after blow-up. Zbl 1108.35092
Fila, M.; Matano, H.; Poláčik, P.
2005
A blow-up result for nonlinear diffusion equations. Zbl 0704.35071
Fila, Marek; Filo, Ján
1989
Stabilization of solutions of certain one-dimensional degenerate diffusion equations. Zbl 0619.35064
Fila, Marek; Filo, Ján
1987
Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed. Zbl 1190.35038
Fila, Marek; Winkler, Michael
2008
Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition. Zbl 1274.35136
Chlebík, Miroslav; Fila, Marek; Reichel, Wolfgang
2003
Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation. Zbl 1321.35102
Fila, Marek; Winkler, Michael
2015
Non-accessible singular homoclinic orbits for a semilinear parabolic equation. Zbl 1340.35179
Fila, Marek; Yanagida, Eiji
2014
Convergence of solutions of a semilinear parabolic equation to selfsimilar solutions of the linear heat equation. Zbl 1178.35068
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2008
The transition from decay to blow-up in some reaction-diffusion-convection equations. Zbl 0849.35057
Fila, Marek; Sacks, Paul
1996
Blow up for a nonlinear degenerate parabolic equation. Zbl 0729.35017
Fila, M.; Filo, J.
1990
Boundedness of global solutions of nonlinear parabolic equations. Zbl 1046.35009
Fila, Marek
2002
Continuation beyond interior gradient blow-up in a semilinear parabolic equation. Zbl 1448.35309
Fila, Marek; Lankeit, Johannes
2020
The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition. Zbl 1446.35046
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki; Lankeit, Johannes
2020
The large diffusion limit for the heat equation with a dynamical boundary condition. Zbl 1450.35031
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2021
The large diffusion limit for the heat equation with a dynamical boundary condition. Zbl 1450.35031
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2021
Lack of smoothing for bounded solutions of a semilinear parabolic equation. Zbl 1436.35243
Fila, Marek; Lankeit, Johannes
2020
Continuation beyond interior gradient blow-up in a semilinear parabolic equation. Zbl 1448.35309
Fila, Marek; Lankeit, Johannes
2020
The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition. Zbl 1446.35046
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki; Lankeit, Johannes
2020
Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition. Zbl 1433.35395
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki; Lankeit, Johannes
2019
A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation. Zbl 1428.26026
Fila, Marek; Winkler, Michael
2019
Solutions with moving singularities for equations of porous medium type. Zbl 1404.35270
Fila, Marek; Takahashi, Jin; Yanagida, Eiji
2019
Slow growth of solutions of superfast diffusion equations with unbounded initial data. Zbl 1386.35178
Fila, Marek; Winkler, Michael
2017
An exterior nonlinear elliptic problem with a dynamical boundary condition. Zbl 1377.35111
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2017
Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation. Zbl 1349.35168
Fila, Marek; Winkler, Michael
2016
Rate of convergence to separable solutions of the fast diffusion equation. Zbl 1348.35120
Fila, Marek; Winkler, Michael
2016
Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1344.35055
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2016
Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1329.35156
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2015
Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation. Zbl 1321.35102
Fila, Marek; Winkler, Michael
2015
Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent. Zbl 1295.35085
Fila, M.; King, J. R.; Winkler, M.
2014
Special asymptotics for a critical fast diffusion equation. Zbl 1284.35239
Fila, Marek; Stuke, Hannes
2014
Non-accessible singular homoclinic orbits for a semilinear parabolic equation. Zbl 1340.35179
Fila, Marek; Yanagida, Eiji
2014
Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition. Zbl 1281.35051
Fila, M.; Ishige, K.; Kawakami, T.
2013
Large-time behavior of small solutions of a two-dimensional semilinear elliptic equation with a dynamical boundary condition. Zbl 1280.35051
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2013
Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition. Zbl 1279.47092
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki
2012
Rate of convergence to Barenblatt profiles for the fast diffusion equation. Zbl 1315.76032
Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji
2012
Grow up and slow decay in the critical Sobolev case. Zbl 1262.35032
Fila, Marek; King, John R.
2012
A continuum of extinction rates for the fast diffusion equation. Zbl 1229.35124
Fila, Marek; Vázquez, Juan-Luis; Winkler, Michael
2011
Homoclinic and heteroclinic orbits for a semilinear parabolic equation. Zbl 1252.35157
Fila, Marek; Yanagida, Eiji
2011
Very slow grow-up of solutions of a semi-linear parabolic equation. Zbl 1221.35064
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2011
Backward selfsimilar solutions of supercritical parabolic equations. Zbl 1173.35547
Fila, Marek; Pulkkinen, Aappo
2009
Boundedness of global solutions of a supercritical parabolic equation. Zbl 1128.35057
Chen, Xinfu; Fila, Marek; Guo, Jong-Shenq
2008
Slow convergence to zero for a parabolic equation with a supercritical nonlinearity. Zbl 1263.35138
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2008
Convergence to self-similar solutions for a semilinear parabolic equation. Zbl 1155.35005
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2008
Rate of convergence to a singular steady state of a supercritical parabolic equation. Zbl 1175.35071
Fila, Marek; Winkler, Michael
2008
Nonconstant selfsimilar blow-up profile for the exponential reaction-diffusion equation. Zbl 1158.35056
Fila, Marek; Pulkkinen, Aappo
2008
Linear behaviour of solutions of a superlinear heat equation. Zbl 1263.35137
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2008
Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed. Zbl 1190.35038
Fila, Marek; Winkler, Michael
2008
Convergence of solutions of a semilinear parabolic equation to selfsimilar solutions of the linear heat equation. Zbl 1178.35068
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2008
Multiple continuation beyond blow-up. Zbl 1212.35231
Fila, Marek; Mizoguchi, Noriko
2007
Convergence to a singular steady state of a parabolic equation with gradient blow-up. Zbl 1125.35367
Fila, Marek; Taskinen, Jari; Winkler, Michael
2007
Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent. Zbl 1170.35456
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2007
Optimal lower bound of the grow-up rate for a supercritical parabolic equation. Zbl 1102.35017
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2006
Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems. Zbl 1120.35048
Fila, Marek; Ninomiya, Hirokazu; Vázquez, Juan Luis
2006
Convergence rate for a parabolic equation with supercritical nonlinearity. Zbl 1087.35049
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2005
Immediate regularization after blow-up. Zbl 1102.35053
Fila, Marek; Matano, Hiroshi; Polácik, Peter
2005
Reaction versus diffusion: Blow-up induced and inhibited by diffusivity. Zbl 1171.35411
Fila, M.; Ninomiya, H.
2005
Blow-up of solutions of supercritical parabolic equations. Zbl 1093.35042
Fila, Marek
2005
Grow-up on the boundary for a semilinear parabolic problem. Zbl 1090.35034
Fila, Marek; Velázquez, Juan J. L.; Winkler, Michael
2005
Immediate regularization after blow-up. Zbl 1108.35092
Fila, M.; Matano, H.; Poláčik, P.
2005
Grow up rate of solutions for a supercritical semilinear diffusion equation. Zbl 1072.35042
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2004
Blow-up of positive solutions of a semilinear parabolic equation with a gradient term. Zbl 1028.35071
Chlebík, Miroslav; Fila, Marek; Quittner, Pavol
2003
Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition. Zbl 1274.35136
Chlebík, Miroslav; Fila, Marek; Reichel, Wolfgang
2003
Blow-up in nonlinear heat equations from the dynamical systems point of view. Zbl 1004.35060
Fila, Marek; Matano, Hiroshi
2002
Complete blow-up and incomplete quenching for the heat equation with a nonlinear boundary condition. Zbl 0994.35066
Fila, Marek; Guo, Jong-Shenq
2002
Existence of $$L^1$$-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054
Fila, Marek; Matano, Hiroshi; Poláčik, Peter
2002
Boundedness of global solutions of nonlinear parabolic equations. Zbl 1046.35009
Fila, Marek
2002
Linear and nonlinear heat equations in $$L^q_\delta$$ spaces and universal bounds for global solutions. Zbl 0993.35023
Fila, Marek; Souplet, Philippe; Weissler, Fred B.
2001
Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Zbl 1006.35103
Fila, Marek; Souplet, Philippe
2001
The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046
Fila, Marek; Souplet, Philippe
2001
Large time behavior of solutions to a quasilinear parabolic equation with a nonlinear boundary condition. Zbl 1194.35055
Fila, Marek; Kawohl, Bernd
2001
On the blow-up rate for the heat equation with a nonlinear boundary condition. Zbl 0980.35073
Chlebík, Miroslav; Fila, Marek
2000
Some recent results on blow-up on the boundary for the heat equation. Zbl 0969.35080
Chlebík, Miroslav; Fila, Marek
2000
Blow-up on the boundary for the heat equation. Zbl 0939.35098
Fila, Marek; Filo, Ján; Lieberman, Gary M.
2000
Connecting equilibria by blow-up solutions. Zbl 1157.35404
Fila, Marek; Matano, Hiroshi
2000
From critical exponents to blow-up rates for parabolic problems. Zbl 0980.35057
Chlebík, M.; Fila, M.
1999
The blow-up rate for a semilinear parabolic system. Zbl 0934.35062
Fila, Marek; Quittner, Pavol
1999
Large time behavior of solutions of a semilinear parabolic equation with a nonlinear dynamical boundary condition. Zbl 0935.35072
Fila, Marek; Quittner, Pavol
1999
Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030
Fila, Marek; Poláčik, Peter
1999
Global solutions of a semilinear parabolic equation. Zbl 0953.35065
Fila, Marek; Poláčik, Peter
1999
Existence of positive solutions of a semilinear elliptic equation in $$\mathbb{R}_+^n$$ with a nonlinear boundary condition. Zbl 0932.35086
Chipot, M.; Chlebík, M.; Fila, M.; Shafrir, I.
1998
A Fujita-type theorem for the Laplace equation with a dynamical boundary condition. Zbl 0922.35053
Amann, H.; Fila, M.
1997
Global solutions of the Laplace equation with a nonlinear dynamical boundary condition. Zbl 0880.35056
Fila, Marek; Quittner, Pavol
1997
On the boundedness of global solutions of abstract semilinear parabolic equations. Zbl 0892.35069
Fila, Marek; Levine, Howard A.
1997
Boundedness of global solutions of nonlocal parabolic equations. Zbl 0902.35055
Fila, Marek
1997
On the solutions to some elliptic equations with nonlinear Neumann boundary conditions. Zbl 0839.35042
Chipot, M.; Shafrir, I.; Fila, M.
1996
Blow-up on the boundary: A survey. Zbl 0858.35065
Fila, Marek; Filo, Ján
1996
On critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition. Zbl 0870.35049
Fila, Marek; Levine, Howard A.
1996
Interior gradient blow-up in a semilinear parabolic equation. Zbl 0864.35052
Angenent, Sigurd B.; Fila, Marek
1996
The transition from decay to blow-up in some reaction-diffusion-convection equations. Zbl 0849.35057
Fila, Marek; Sacks, Paul
1996
On critical exponents for a system of heat equations coupled in the boundary conditions. Zbl 0824.35048
Deng, K.; Fila, M.; Levine, H. A.
1994
Derivative blow-up and beyond for quasilinear parabolic equations. Zbl 0811.35059
Fila, Marek; Lieberman, Gary M.
1994
A Fujita-type global existence – global non-existence theorem for a system of reaction diffusion equations with differing diffusivities. Zbl 0814.35046
Fila, Marek; Levine, Howard A.; Uda, Yoshitaka
1994
Quenching on the boundary. Zbl 0809.35043
Fila, Marek; Levine, Howard A.
1993
Stabilization of solutions of weakly singular quenching problems. Zbl 0785.35054
Fila, Marek; Levine, Howard A.; Vazquez, Juan L.
1993
Radial positive solutions for a semilinear elliptic equation with a gradient term. Zbl 0803.35035
Fila, M.; Quittner, P.
1993
Boundedness of global solutions of nonlinear diffusion equations. Zbl 0764.35010
Fila, Marek
1992
Quenching for quasilinear equations. Zbl 0801.35057
Fila, Marek; Kawohl, Bernhard; Levine, Howard A.
1992
Asymptotic analysis of quenching problems. Zbl 0798.35079
Fila, Marek; Kawohl, Bernhard
1992
The quenching problem on the $$N$$-dimensional ball. Zbl 0792.35097
Fila, Marek; Hulshof, Josephus; Quittner, Pavol
1992
Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Zbl 0743.35038
Chipot, M.; Fila, M.; Quittner, P.
1991
The blow-up rate for the heat equation with a nonlinear boundary condition. Zbl 0735.35014
Fila, Marek; Quittner, Pavol
1991
Remarks on blow up for a nonlinear parabolic equation with a gradient term. Zbl 0768.35047
Fila, Marek
1991
A note on the quenching rate. Zbl 0727.35007
Fila, Marek; Hulshof, Josephus
1991
Is quenching in infinite time possible? Zbl 0737.35005
Fila, Marek; Kawohl, Bernhard
1990
Blow up for a nonlinear degenerate parabolic equation. Zbl 0729.35017
Fila, M.; Filo, J.
1990
Boundedness of global solutions for the heat equation with nonlinear boundary conditions. Zbl 0702.35141
Fila, Marek
1989
A blow-up result for nonlinear diffusion equations. Zbl 0704.35071
Fila, Marek; Filo, Ján
1989
Stabilization of solutions of certain one-dimensional degenerate diffusion equations. Zbl 0619.35064
Fila, Marek; Filo, Ján
1987
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### 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
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### 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
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### 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)