## Poláčik, Peter

Compute Distance To:
 Author ID: polacik.peter Published as: Poláčik, Peter; Poláčik, P.; Polácik, Peter; Polacik, Peter; Poláçik, Peter; Polácik, P. more...less External Links: MGP
 Documents Indexed: 107 Publications since 1987, including 2 Books 1 Contribution as Editor Reviewing Activity: 155 Reviews Co-Authors: 39 Co-Authors with 71 Joint Publications 1,139 Co-Co-Authors
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### Co-Authors

 35 single-authored 10 Yanagida, Eiji 8 Quittner, Pavol 6 Fila, Marek 6 Matano, Hiroshi 5 Brunovský, Pavol 5 Valdebenito, Darío A. 4 Földes, Juraj 4 Húska, Juraj 3 Lou, Yuan 3 Tereščák, Ignác 2 Chen, Xu-Yan 2 Du, Yihong 2 Hutson, Vivian 2 Jendoubi, Mohamed Ali 2 Mischaikow, Konstantin 2 Pauthier, Antoine 2 Rybakowski, Krzysztof P. 2 Safonov, Mikhail V. 2 Souplet, Philippe 1 Bartsch, Thomas J. 1 Busca, Jérôme 1 Chen, Chiun-Chuan 1 Dancer, Edward Norman 1 Feireisl, Eduard 1 Fiedler, Bernold 1 Haraux, Alain 1 Martínez, Salomé 1 Mierczyński, Janusz 1 Mora, Xavier 1 Ni, Wei-Ming 1 Ninomiya, Hirokazu 1 Peng, Rui 1 Raugel, Geneviève 1 Sandstede, Björn 1 Simondon, Frédérique 1 Solà-Morales, Joan 1 Šošovička, Vladimír 1 Šverák, Vladimír 1 Terracini, Susanna
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### Serials

 13 Journal of Differential Equations 8 Journal of Dynamics and Differential Equations 8 Discrete and Continuous Dynamical Systems 6 Communications in Partial Differential Equations 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 SIAM Journal on Mathematical Analysis 3 Archive for Rational Mechanics and Analysis 3 Indiana University Mathematics Journal 3 Journal of Functional Analysis 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Memoirs of the American Mathematical Society 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Differential and Integral Equations 2 Acta Mathematica Universitatis Comenianae. New Series 2 Advances in Differential Equations 2 Nonlinear Analysis. Theory, Methods & Applications 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Biology 1 Nonlinearity 1 Commentationes Mathematicae Universitatis Carolinae 1 Duke Mathematical Journal 1 Mathematische Zeitschrift 1 Transactions of the American Mathematical Society 1 Asymptotic Analysis 1 Mathematica Bohemica 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Tatra Mountains Mathematical Publications 1 Electronic Journal of Qualitative Theory of Differential Equations 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Evolution Equations 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Journal of Fixed Point Theory and Applications 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S
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### Fields

 104 Partial differential equations (35-XX) 18 Dynamical systems and ergodic theory (37-XX) 9 Global analysis, analysis on manifolds (58-XX) 4 Ordinary differential equations (34-XX) 4 Biology and other natural sciences (92-XX) 3 Operator theory (47-XX) 2 Algebraic topology (55-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 General topology (54-XX) 1 Fluid mechanics (76-XX)

### Citations contained in zbMATH Open

98 Publications have been cited 1,480 times in 872 Documents Cited by Year
Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
2007
The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035
Hutson, V.; Mischaikow, K.; Poláčik, P.
2001
Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
2007
On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055
Poláčik, Peter; Yanagida, Eiji
2003
Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039
Poláčik, P.; Tereščák, I.
1991
Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002
Poláčik, P.; Tereščák, Ignác
1993
Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064
Poláčik, Peter
1989
Competing species near a degenerate limit. Zbl 1043.35080
Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P.
2003
Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059
Chen, Xu-Yan; Poláčik, Peter
1996
Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060
Fiedler, Bernold; Poláčik, Peter
1990
Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054
Poláčik, Peter; Rybakowski, Krzysztof P.
1996
Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001
Poláčik, P.
2002
The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062
Brunovský, P.; Poláčik, P.
1997
Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009
Brunovský, P.; Poláčik, P.; Sandstede, B.
1992
On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098
Földes, J.; Poláčik, Peter
2009
Convergence to equilibrium for semilinear parabolic problems in $$\mathbb{R}^N$$. Zbl 1021.35013
Busca, J.; Jendoubi, M. A.; Poláčik, P.
2002
Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011
Lou, Yuan; Martínez, Salomé; Poláčik, Peter
2006
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041
Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol
2011
A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045
Poláčik, Peter; Quittner, Pavol
2006
Threshold solutions and sharp transitions for nonautonomous parabolic equations on $${\mathbb{R}^N}$$. Zbl 1262.35130
Poláčik, P.
2011
A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044
Poláčik, P.; Yanagida, E.
2005
Monotonicity of stable solutions in shadow systems. Zbl 0981.35018
Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji
2001
Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049
Hess, Peter; Poláčik, P.
1994
Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011
Haraux, A.; Poláčik, P.
1992
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046
Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V.
2007
Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on $$\mathbb{R}$$. Zbl 0987.35079
Feireisl, Eduard; Poláčik, Peter
2000
Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046
Poláčik, P.; Simondon, F.
2002
Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027
Poláčik, Peter
1991
Immediate regularization after blow-up. Zbl 1102.35053
Fila, Marek; Matano, Hiroshi; Polácik, Peter
2005
Locally uniform convergence to an equilibrium for nonlinear parabolic equations on $$\mathbb{R}^N$$. Zbl 1336.35207
Du, Yihong; Poláčik, Peter
2015
Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077
Hess, Peter; Poláčik, Peter
1993
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part I: A general quasiconvergence theorem and its consequences. Zbl 1345.35052
Matano, H.; Poláčik, P.
2016
Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008
Poláčik, P.; Tereščák, I.
1994
On the local structure of $$\omega$$-limit sets of maps. Zbl 0889.34048
Brunovský, P.; Poláčik, P.
1997
High-dimensional $$\omega$$-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060
Poláčik, Peter
1995
Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073
Chen, Xu-Yan; Poláčik, Peter
1995
Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042
Poláčik, P.
2009
Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063
Poláčik, Peter
2007
The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353
Húska, Juraj; Poláčik, Peter
2004
Symmetry properties of positive solutions of parabolic equations on $$\mathbb R^N$$. I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045
Poláčik, P.
2005
Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $$\mathbb{R}^ 3$$. Zbl 0774.35041
Poláčik, Peter
1991
Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060
Dancer, E. N.; Poláčik, P.
1999
Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037
Poláčik, Peter; Quittner, Pavol
2005
Existence of quasiperiodic solutions of elliptic equations on $$\mathbb{R}^{N + 1}$$ via center manifold and KAM theorems. Zbl 1372.35016
Poláčik, Peter; Valdebenito, Darío A.
2017
Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on $${\mathbb{R}}$$. Zbl 1319.35097
Poláčik, P.
2015
Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045
Jendoubi, M. A.; Poláčik, P.
2003
Convergence to a steady state for asymptotically autonomous semilinear heat equations on $$\mathbb R^N$$. Zbl 1263.35035
Földes, Juraj; Poláčik, P.
2011
Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 1456.35039
Poláčik, P.
2016
Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030
Fila, Marek; Poláčik, Peter
1999
Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153
Poláčik, P.; Šverák, V.
2008
Symmetry properties of positive solutions of parabolic equations on $$\mathbb R^N$$. II: Entire solutions. Zbl 1128.35051
Poláčik, P.
2006
On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030
Poláčik, P.
2005
Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046
Poláčik, P.
1992
Morse indices and bifurcations of positive solutions of $$\Delta u+f(u)=0$$ on $$\mathbb R^ N$$. Zbl 1101.35321
Poláčik, Peter
2001
Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 06780933
Poláčik, P.
2017
Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036
Poláčik, Peter
1989
Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403
Poláčik, P.; Yanagida, E.
2004
An entire solution of a bistable parabolic equation on $$\mathbb{R}$$ with two colliding pulses. Zbl 1362.35152
Matano, H.; Poláčik, P.
2017
Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on $$\mathbb{R}$$. Zbl 1450.35002
Poláčik, Peter
2020
The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127
Du, Yihong; Peng, Rui; Poláçik, Peter
2012
Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148
Poláčik, Peter; Yanagida, Eiji
2014
Global solutions of a semilinear parabolic equation. Zbl 0953.35065
Fila, Marek; Poláčik, Peter
1999
Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041
Poláčik, Peter
1994
Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions. Zbl 0639.35039
Poláčik, Peter
1987
Group actions on strongly monotone dynamical systems. Zbl 0642.58031
Mierczyński, Janusz; Poláčik, Peter
1989
Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074
Poláčik, Peter; Rybakowski, Krzysztof
1995
Existence of $$L^1$$-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054
Fila, Marek; Matano, Hiroshi; Poláčik, Peter
2002
Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109
Poláčik, P.; Terracini, Susanna
2014
Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083
Poláčik, P.
2011
On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073
Poláčik, P.
2012
Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065
1996
Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013
Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J.
1991
Generic hyperbolicity for reaction diffusion equations on symmetric domains. Zbl 0622.35005
Brunovský, Pavol; Poláčik, Peter
1987
Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109
Poláčik, Peter; Yanagida, Eiji
2014
On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034
Poláčik, Peter
2014
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076
Pauthier, Antoine; Poláčik, Peter
2018
Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130
Poláčik, Peter
2015
Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023
Poláčik, Peter; Yanagida, Eiji
2001
Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150
Poláčik, Peter; Yanagida, Eiji
2009
Exponential separation and principal Floquet bundles for linear parabolic equations on $$\mathbb R^N$$. Zbl 1170.35021
Húska, Juraj; Poláčik, Peter
2008
Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014
Poláčik, Peter; Quittner, Pavol
2008
Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391
Húska, J.; Poláčik, P.; Safonov, M. V.
2005
Immediate regularization after blow-up. Zbl 1108.35092
Fila, M.; Matano, H.; Poláčik, P.
2005
Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304
Poláčik, P.
2020
Entire and ancient solutions of a supercritical semilinear heat equation. Zbl 1458.35228
Poláčik, Peter; Quittner, Pavol
2021
Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065
Poláčik, Peter
1994
Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051
Poláčik, Peter; Yanagida, Eiji
2002
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009
Poláčik, P.
2002
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054
Poláčik, Peter
1990
Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093
Poláčik, P.
2017
Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Zbl 1439.35026
Poláčik, Peter; Valdebenito, Darío A.
2020
Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074
Poláčik, P.
2012
On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170
Poláčik, P.; Quittner, P.
2020
Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097
Poláčik, Peter
1999
Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043
Poláčik, P.
1990
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. II: Generic nonlinearities. Zbl 1439.35200
Matano, H.; Poláčik, P.
2020
On asymptotically symmetric parabolic equations. Zbl 1262.35041
Földes, Juraj; Poláčik, Peter
2012
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity. Zbl 1473.35056
Pauthier, Antoine; Poláčik, Peter
2021
Entire and ancient solutions of a supercritical semilinear heat equation. Zbl 1458.35228
Poláčik, Peter; Quittner, Pavol
2021
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity. Zbl 1473.35056
Pauthier, Antoine; Poláčik, Peter
2021
Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on $$\mathbb{R}$$. Zbl 1450.35002
Poláčik, Peter
2020
Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304
Poláčik, P.
2020
Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Zbl 1439.35026
Poláčik, Peter; Valdebenito, Darío A.
2020
On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170
Poláčik, P.; Quittner, P.
2020
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. II: Generic nonlinearities. Zbl 1439.35200
Matano, H.; Poláčik, P.
2020
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076
Pauthier, Antoine; Poláčik, Peter
2018
Existence of quasiperiodic solutions of elliptic equations on $$\mathbb{R}^{N + 1}$$ via center manifold and KAM theorems. Zbl 1372.35016
Poláčik, Peter; Valdebenito, Darío A.
2017
Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 06780933
Poláčik, P.
2017
An entire solution of a bistable parabolic equation on $$\mathbb{R}$$ with two colliding pulses. Zbl 1362.35152
Matano, H.; Poláčik, P.
2017
Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093
Poláčik, P.
2017
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part I: A general quasiconvergence theorem and its consequences. Zbl 1345.35052
Matano, H.; Poláčik, P.
2016
Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 1456.35039
Poláčik, P.
2016
Locally uniform convergence to an equilibrium for nonlinear parabolic equations on $$\mathbb{R}^N$$. Zbl 1336.35207
Du, Yihong; Poláčik, Peter
2015
Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on $${\mathbb{R}}$$. Zbl 1319.35097
Poláčik, P.
2015
Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130
Poláčik, Peter
2015
Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148
Poláčik, Peter; Yanagida, Eiji
2014
Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109
Poláčik, P.; Terracini, Susanna
2014
Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109
Poláčik, Peter; Yanagida, Eiji
2014
On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034
Poláčik, Peter
2014
The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127
Du, Yihong; Peng, Rui; Poláçik, Peter
2012
On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073
Poláčik, P.
2012
Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074
Poláčik, P.
2012
On asymptotically symmetric parabolic equations. Zbl 1262.35041
Földes, Juraj; Poláčik, Peter
2012
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041
Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol
2011
Threshold solutions and sharp transitions for nonautonomous parabolic equations on $${\mathbb{R}^N}$$. Zbl 1262.35130
Poláčik, P.
2011
Convergence to a steady state for asymptotically autonomous semilinear heat equations on $$\mathbb R^N$$. Zbl 1263.35035
Földes, Juraj; Poláčik, P.
2011
Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083
Poláčik, P.
2011
On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098
Földes, J.; Poláčik, Peter
2009
Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042
Poláčik, P.
2009
Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150
Poláčik, Peter; Yanagida, Eiji
2009
Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153
Poláčik, P.; Šverák, V.
2008
Exponential separation and principal Floquet bundles for linear parabolic equations on $$\mathbb R^N$$. Zbl 1170.35021
Húska, Juraj; Poláčik, Peter
2008
Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014
Poláčik, Peter; Quittner, Pavol
2008
Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
2007
Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
2007
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046
Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V.
2007
Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063
Poláčik, Peter
2007
Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011
Lou, Yuan; Martínez, Salomé; Poláčik, Peter
2006
A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045
Poláčik, Peter; Quittner, Pavol
2006
Symmetry properties of positive solutions of parabolic equations on $$\mathbb R^N$$. II: Entire solutions. Zbl 1128.35051
Poláčik, P.
2006
A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044
Poláčik, P.; Yanagida, E.
2005
Immediate regularization after blow-up. Zbl 1102.35053
Fila, Marek; Matano, Hiroshi; Polácik, Peter
2005
Symmetry properties of positive solutions of parabolic equations on $$\mathbb R^N$$. I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045
Poláčik, P.
2005
Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037
Poláčik, Peter; Quittner, Pavol
2005
On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030
Poláčik, P.
2005
Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391
Húska, J.; Poláčik, P.; Safonov, M. V.
2005
Immediate regularization after blow-up. Zbl 1108.35092
Fila, M.; Matano, H.; Poláčik, P.
2005
The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353
Húska, Juraj; Poláčik, Peter
2004
Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403
Poláčik, P.; Yanagida, E.
2004
On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055
Poláčik, Peter; Yanagida, Eiji
2003
Competing species near a degenerate limit. Zbl 1043.35080
Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P.
2003
Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045
Jendoubi, M. A.; Poláčik, P.
2003
Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001
Poláčik, P.
2002
Convergence to equilibrium for semilinear parabolic problems in $$\mathbb{R}^N$$. Zbl 1021.35013
Busca, J.; Jendoubi, M. A.; Poláčik, P.
2002
Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046
Poláčik, P.; Simondon, F.
2002
Existence of $$L^1$$-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054
Fila, Marek; Matano, Hiroshi; Poláčik, Peter
2002
Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051
Poláčik, Peter; Yanagida, Eiji
2002
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009
Poláčik, P.
2002
The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035
Hutson, V.; Mischaikow, K.; Poláčik, P.
2001
Monotonicity of stable solutions in shadow systems. Zbl 0981.35018
Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji
2001
Morse indices and bifurcations of positive solutions of $$\Delta u+f(u)=0$$ on $$\mathbb R^ N$$. Zbl 1101.35321
Poláčik, Peter
2001
Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023
Poláčik, Peter; Yanagida, Eiji
2001
Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on $$\mathbb{R}$$. Zbl 0987.35079
Feireisl, Eduard; Poláčik, Peter
2000
Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060
Dancer, E. N.; Poláčik, P.
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
Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097
Poláčik, Peter
1999
The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062
Brunovský, P.; Poláčik, P.
1997
On the local structure of $$\omega$$-limit sets of maps. Zbl 0889.34048
Brunovský, P.; Poláčik, P.
1997
Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059
Chen, Xu-Yan; Poláčik, Peter
1996
Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054
Poláčik, Peter; Rybakowski, Krzysztof P.
1996
Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065
1996
High-dimensional $$\omega$$-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060
Poláčik, Peter
1995
Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073
Chen, Xu-Yan; Poláčik, Peter
1995
Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074
Poláčik, Peter; Rybakowski, Krzysztof
1995
Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049
Hess, Peter; Poláčik, P.
1994
Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008
Poláčik, P.; Tereščák, I.
1994
Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041
Poláčik, Peter
1994
Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065
Poláčik, Peter
1994
Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002
Poláčik, P.; Tereščák, Ignác
1993
Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077
Hess, Peter; Poláčik, Peter
1993
Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009
Brunovský, P.; Poláčik, P.; Sandstede, B.
1992
Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011
Haraux, A.; Poláčik, P.
1992
Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046
Poláčik, P.
1992
Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039
Poláčik, P.; Tereščák, I.
1991
Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027
Poláčik, Peter
1991
Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $$\mathbb{R}^ 3$$. Zbl 0774.35041
Poláčik, Peter
1991
Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013
Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J.
1991
Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060
Fiedler, Bernold; Poláčik, Peter
1990
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054
Poláčik, Peter
1990
Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043
Poláčik, P.
1990
Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064
Poláčik, Peter
1989
Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036
Poláčik, Peter
1989
Group actions on strongly monotone dynamical systems. Zbl 0642.58031
Mierczyński, Janusz; Poláčik, Peter
1989
Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions. Zbl 0639.35039
Poláčik, Peter
1987
Generic hyperbolicity for reaction diffusion equations on symmetric domains. Zbl 0622.35005
Brunovský, Pavol; Poláčik, Peter
1987
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### Cited by 870 Authors

 49 Poláčik, Peter 30 Lou, Yuan 20 Shen, Wenxian 17 Yanagida, Eiji 14 Winkler, Michael 13 Fila, Marek 13 Peng, Rui 12 Matano, Hiroshi 12 Wang, Yi 12 Wei, Juncheng 11 Du, Yihong 11 Mizoguchi, Noriko 11 Obaya, Rafael 11 Quittner, Pavol 11 Souplet, Philippe 10 Ishige, Kazuhiro 10 Li, Wan-Tong 10 Lou, Bendong 10 Mierczyński, Janusz 10 Phan, Quoc Hung 10 Weth, Tobias 9 Jendoubi, Mohamed Ali 9 Sanz, Ana M. 9 Villavert, John 9 Zhou, Maolin 8 Jiang, Jifa 8 Lam, King-Yeung 8 Yi, Taishan 8 Zou, Wenming 7 Cantrell, Robert Stephen 7 Chill, Ralph 7 Cosner, Chris 7 Guo, Zongming 7 Harrabi, Abdellaziz 7 Shi, Junping 7 Smith, Hal Leslie 7 Vishnevskii, Mikhail P. 7 Wang, Zhi Cheng 7 Zhao, Xiao-Qiang 6 Dai, Wei 6 Földes, Juraj 6 Giletti, Thomas 6 Liu, Shuang 6 Wang, Yuxia 6 Wu, Jianhua 5 Dancer, Edward Norman 5 Ding, Weiwei 5 Duong, Anh Tuan 5 Fiedler, Bernold 5 Giga, Yoshikazu 5 Grasselli, Maurizio 5 Hamel, François 5 Jänig, Axel 5 Kawakami, Tatsuki 5 Langa, Jose’ Antonio 5 Lin, Guo 5 Nadin, Grégoire 5 Rodríguez-Bernal, Aníbal 5 Ruan, Shigui 5 Vazquez, Juan Luis 5 Wang, Mingxin 5 Wu, Hao 5 Yang, Hui 5 Zhang, Zhitao 5 Zhou, Dun 4 Alfaro, Matthieu 4 Bo, Wei-Jian 4 Cholewa, Jan W. 4 Del Pino, Manuel A. 4 Ducrot, Arnaud 4 Dupaigne, Louis 4 Farina, Alberto 4 Fujishima, Yohei 4 García-Melián, Jorge 4 Huang, Haochuan 4 Huang, Rui 4 Húska, Juraj 4 Joly, Romain 4 Li, Congming 4 Li, Kui 4 Li, Yimei 4 Miyamoto, Yasuhito 4 Mtiri, Foued 4 Naito, Yūki 4 Nolasco de Carvalho, Alexandre 4 Qin, Guolin 4 Rocha, Carlos 4 Roquejoffre, Jean-Michel 4 Saldaña, Alberto 4 Valdebenito, Darío A. 4 Vétois, Jérôme 4 Wan, FangShu 4 Wu, Jianhong 4 Wu, YiXiang 4 Yin, Jingxue 4 Zhang, Zhengce 4 Zheng, Gao-Feng 4 Zheng, Songmu 3 Arrieta, José M. 3 Bao, Jiguang ...and 770 more Authors
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### Cited in 153 Serials

 142 Journal of Differential Equations 47 Journal of Dynamics and Differential Equations 46 Journal of Mathematical Analysis and Applications 44 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 29 Discrete and Continuous Dynamical Systems 27 Calculus of Variations and Partial Differential Equations 21 Communications on Pure and Applied Analysis 19 Journal of Functional Analysis 18 Journal of Mathematical Biology 17 Transactions of the American Mathematical Society 16 Nonlinear Analysis. Real World Applications 15 Proceedings of the American Mathematical Society 15 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 15 Discrete and Continuous Dynamical Systems. Series B 14 Mathematische Annalen 14 Journal de Mathématiques Pures et Appliquées. Neuvième Série 13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 12 Communications in Contemporary Mathematics 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Advances in Mathematics 11 Communications in Partial Differential Equations 11 NoDEA. Nonlinear Differential Equations and Applications 11 Journal of Evolution Equations 9 Archive for Rational Mechanics and Analysis 9 SIAM Journal on Mathematical Analysis 8 Nonlinearity 8 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Bulletin of Mathematical Biology 7 Advances in Difference Equations 6 Siberian Mathematical Journal 6 Applied Mathematics Letters 6 Advances in Nonlinear Analysis 5 Applicable Analysis 5 Journal of Difference Equations and Applications 5 Journal of Biological Dynamics 5 Science China. Mathematics 4 Journal d’Analyse Mathématique 4 Mathematical Biosciences 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Memoirs of the American Mathematical Society 4 Acta Applicandae Mathematicae 4 SIAM Journal on Applied Mathematics 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Advanced Nonlinear Studies 4 Milan Journal of Mathematics 4 Boundary Value Problems 4 Complex Variables and Elliptic Equations 4 Discrete and Continuous Dynamical Systems. Series S 3 Communications in Mathematical Physics 3 Rocky Mountain Journal of Mathematics 3 Chaos, Solitons and Fractals 3 Archiv der Mathematik 3 Journal of Computational and Applied Mathematics 3 Physica D 3 Journal of Nonlinear Science 3 Topological Methods in Nonlinear Analysis 3 Mathematical Biosciences and Engineering 3 Journal of Fixed Point Theory and Applications 3 Journal of Elliptic and Parabolic Equations 2 Bulletin of the Australian Mathematical Society 2 Computers & Mathematics with Applications 2 Journal of Mathematical Physics 2 Mathematical Methods in the Applied Sciences 2 Mathematical Notes 2 Acta Mathematica 2 Journal of the Korean Mathematical Society 2 Manuscripta Mathematica 2 Mathematische Nachrichten 2 Monatshefte für Mathematik 2 Pacific Journal of Mathematics 2 Quarterly of Applied Mathematics 2 Tohoku Mathematical Journal. Second Series 2 Chinese Annals of Mathematics. Series B 2 Journal of Integral Equations and Applications 2 Electronic Journal of Differential Equations (EJDE) 2 Bulletin des Sciences Mathématiques 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Taiwanese Journal of Mathematics 2 Revista Matemática Complutense 2 Journal of the European Mathematical Society (JEMS) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Proceedings of the Steklov Institute of Mathematics 2 Analysis and Mathematical Physics 2 AIMS Mathematics 2 Mathematics in Engineering 2 SN Partial Differential Equations and Applications 1 Communications on Pure and Applied Mathematics 1 Journal of Statistical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Journal of Geometry and Physics 1 Applied Mathematics and Computation 1 Automatica 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 Duke Mathematical Journal 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik ...and 53 more Serials
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### Cited in 31 Fields

 752 Partial differential equations (35-XX) 178 Biology and other natural sciences (92-XX) 139 Dynamical systems and ergodic theory (37-XX) 74 Ordinary differential equations (34-XX) 35 Operator theory (47-XX) 26 Integral equations (45-XX) 22 Global analysis, analysis on manifolds (58-XX) 11 Fluid mechanics (76-XX) 10 Numerical analysis (65-XX) 8 Difference and functional equations (39-XX) 8 Functional analysis (46-XX) 8 Systems theory; control (93-XX) 7 Probability theory and stochastic processes (60-XX) 6 Potential theory (31-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Differential geometry (53-XX) 6 General topology (54-XX) 6 Classical thermodynamics, heat transfer (80-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Real functions (26-XX) 5 Mechanics of particles and systems (70-XX) 4 Mechanics of deformable solids (74-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Quantum theory (81-XX) 2 Combinatorics (05-XX) 2 Functions of a complex variable (30-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX)