Edit Profile Poláčik, Peter Compute Distance To: Compute Author ID: polacik.peter Published as: Polacik, Peter; Polácik, P.; Polácik, Peter; Poláçik, Peter; Poláčik, P.; Poláčik, Peter External Links: MGP Documents Indexed: 105 Publications since 1987, including 2 Books Reviewing Activity: 155 Reviews all top 5 Co-Authors 35 single-authored 10 Yanagida, Eiji 8 Quittner, Pavol 6 Fila, Marek 6 Matano, Hiroshi 5 Brunovský, Pavol 4 Földes, Juraj 4 Húska, Juraj 3 Lou, Yuan 3 Tereščák, Ignác 3 Valdebenito, Darío A. 2 Chen, Xu-Yan 2 Du, Yihong 2 Hutson, Vivian 2 Jendoubi, Mohamed Ali 2 Mischaikow, Konstantin 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 Hess, Peter 1 Hess, Peter O. 1 Martínez, Salomé 1 Mierczyński, Janusz 1 Mora, Xavier 1 Ni, Wei-Ming 1 Ninomiya, Hirokazu 1 Pauthier, Antoine 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 1 Wang, Xuefeng all top 5 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 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 Journal of Functional Analysis 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 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 Journal of Fixed Point Theory and Applications 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S all top 5 Fields 101 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 94 Publications have been cited 1,348 times in 783 Documents Cited by ▼ Year ▼ Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 150 2007 The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035Hutson, V.; Mischaikow, K.; Poláčik, P. 79 2001 On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055Poláčik, Peter; Yanagida, Eiji 60 2003 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 57 2007 Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039Poláčik, P.; Tereščák, I. 48 1991 Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002Poláčik, P.; Tereščák, Ignác 44 1993 Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064Poláčik, Peter 40 1989 Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059Chen, Xu-Yan; Poláčik, Peter 33 1996 Competing species near a degenerate limit. Zbl 1043.35080Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P. 32 2003 Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060Fiedler, Bernold; Poláčik, Peter 31 1990 Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054Poláčik, Peter; Rybakowski, Krzysztof P. 30 1996 The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062Brunovský, P.; Poláčik, P. 28 1997 Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001Poláčik, P. 27 2002 Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009Brunovský, P.; Poláčik, P.; Sandstede, B. 26 1992 Convergence to equilibrium for semilinear parabolic problems in \(\mathbb{R}^N\). Zbl 1021.35013Busca, J.; Jendoubi, M. A.; Poláčik, P. 25 2002 On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098Földes, J.; Poláčik, Peter 22 2009 Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011Lou, Yuan; Martínez, Salomé; Poláčik, Peter 22 2006 A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045Poláčik, Peter; Quittner, Pavol 22 2006 Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\). Zbl 1262.35130Poláčik, P. 20 2011 Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol 20 2011 A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044Poláčik, P.; Yanagida, E. 19 2005 Monotonicity of stable solutions in shadow systems. Zbl 0981.35018Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji 19 2001 Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049Hess, Peter; Poláčik, P. 19 1994 Immediate regularization after blow-up. Zbl 1102.35053Fila, Marek; Matano, Hiroshi; Polácik, Peter 18 2005 Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V. 17 2007 Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046Poláčik, P.; Simondon, F. 17 2002 Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on \(\mathbb{R}\). Zbl 0987.35079Feireisl, Eduard; Poláčik, Peter 17 2000 Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011Haraux, A.; Poláčik, P. 17 1992 Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027Poláčik, Peter 17 1991 Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077Hess, Peter; Poláčik, Peter 15 1993 Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008Poláčik, P.; Tereščák, I. 14 1994 Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part I: A general quasiconvergence theorem and its consequences. Zbl 1345.35052Matano, H.; Poláčik, P. 13 2016 Locally uniform convergence to an equilibrium for nonlinear parabolic equations on \(\mathbb{R}^N\). Zbl 1336.35207Du, Yihong; Poláčik, Peter 13 2015 On the local structure of \(\omega\)-limit sets of maps. Zbl 0889.34048Brunovský, P.; Poláčik, P. 12 1997 The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353Húska, Juraj; Poláčik, Peter 11 2004 Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042Poláčik, P. 10 2009 Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063Poláčik, Peter 10 2007 High-dimensional \(\omega\)-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060Poláčik, Peter 10 1995 Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060Dancer, E. N.; Poláčik, P. 9 1999 Realization of any finite jet in a scalar semilinear parabolic equation on the ball in \(\mathbb{R}^ 3\). Zbl 0774.35041Poláčik, Peter 9 1991 Convergence to a steady state for asymptotically autonomous semilinear heat equations on \(\mathbb R^N\). Zbl 1263.35035Földes, Juraj; Poláčik, P. 8 2011 Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037Poláčik, Peter; Quittner, Pavol 8 2005 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045Poláčik, P. 8 2005 On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030Poláčik, P. 8 2005 Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045Jendoubi, M. A.; Poláčik, P. 8 2003 Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030Fila, Marek; Poláčik, Peter 8 1999 Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems. Zbl 1372.35016Poláčik, Peter; Valdebenito, Darío A. 7 2017 Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 06643365Poláčik, P. 7 2016 Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\). Zbl 1319.35097Poláčik, P. 7 2015 The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127Du, Yihong; Peng, Rui; Poláçik, Peter 7 2012 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). II: Entire solutions. Zbl 1128.35051Poláčik, P. 7 2006 Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403Poláčik, P.; Yanagida, E. 7 2004 Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073Chen, Xu-Yan; Poláčik, Peter 7 1995 Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046Poláčik, P. 7 1992 Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036Poláčik, Peter 7 1989 Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148Poláčik, Peter; Yanagida, Eiji 6 2014 Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153Poláčik, P.; Šverák, V. 6 2008 Morse indices and bifurcations of positive solutions of \(\Delta u+f(u)=0\) on \(\mathbb R^ N\). Zbl 1101.35321Poláčik, Peter 6 2001 Global solutions of a semilinear parabolic equation. Zbl 0953.35065Fila, Marek; Poláčik, Peter 6 1999 Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041Poláčik, Peter 6 1994 Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions. Zbl 0639.35039Poláčik, Peter 6 1987 An entire solution of a bistable parabolic equation on \(\mathbb{R}\) with two colliding pulses. Zbl 1362.35152Matano, H.; Poláčik, P. 5 2017 On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073Poláčik, P. 5 2012 Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083Poláčik, P. 5 2011 Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054Fila, Marek; Matano, Hiroshi; Poláčik, Peter 5 2002 Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074Poláčik, Peter; Rybakowski, Krzysztof 5 1995 Group actions on strongly monotone dynamical systems. Zbl 0642.58031Mierczyński, Janusz; Poláčik, Peter 5 1989 Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 06780933Poláčik, P. 4 2017 Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109Poláčik, P.; Terracini, Susanna 4 2014 On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034Poláčik, Peter 4 2014 Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\). Zbl 1170.35021Húska, Juraj; Poláčik, Peter 4 2008 Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065Poláčik, Peter; Šošovička, Vladimír 4 1996 Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J. 4 1991 Generic hyperbolicity for reaction diffusion equations on symmetric domains. Zbl 0622.35005Brunovský, Pavol; Poláčik, Peter 4 1987 Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on \(\mathbb{R}\). Zbl 1450.35002Poláčik, Peter 3 2020 Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109Poláčik, Peter; Yanagida, Eiji 3 2014 Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150Poláčik, Peter; Yanagida, Eiji 3 2009 Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014Poláčik, Peter; Quittner, Pavol 3 2008 Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391Húska, J.; Poláčik, P.; Safonov, M. V. 3 2005 Immediate regularization after blow-up. Zbl 1108.35092Fila, M.; Matano, H.; Poláčik, P. 3 2005 Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023Poláčik, Peter; Yanagida, Eiji 3 2001 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076Pauthier, Antoine; Poláčik, Peter 2 2018 Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074Poláčik, P. 2 2012 Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009Poláčik, P. 2 2002 Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051Poláčik, Peter; Yanagida, Eiji 2 2002 Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065Poláčik, Peter 2 1994 Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054Poláčik, Peter 2 1990 Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043Poláčik, P. 2 1990 Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304Poláčik, P. 1 2020 On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170Poláčik, P.; Quittner, P. 1 2020 Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093Poláčik, P. 1 2017 Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130Poláčik, Peter 1 2015 On asymptotically symmetric parabolic equations. Zbl 1262.35041Földes, Juraj; Poláčik, Peter 1 2012 Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097Poláčik, Peter 1 1999 Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on \(\mathbb{R}\). Zbl 1450.35002Poláčik, Peter 3 2020 Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304Poláčik, P. 1 2020 On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170Poláčik, P.; Quittner, P. 1 2020 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076Pauthier, Antoine; Poláčik, Peter 2 2018 Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems. Zbl 1372.35016Poláčik, Peter; Valdebenito, Darío A. 7 2017 An entire solution of a bistable parabolic equation on \(\mathbb{R}\) with two colliding pulses. Zbl 1362.35152Matano, H.; Poláčik, P. 5 2017 Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 06780933Poláčik, P. 4 2017 Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093Poláčik, P. 1 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 1345.35052Matano, H.; Poláčik, P. 13 2016 Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 06643365Poláčik, P. 7 2016 Locally uniform convergence to an equilibrium for nonlinear parabolic equations on \(\mathbb{R}^N\). Zbl 1336.35207Du, Yihong; Poláčik, Peter 13 2015 Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\). Zbl 1319.35097Poláčik, P. 7 2015 Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130Poláčik, Peter 1 2015 Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148Poláčik, Peter; Yanagida, Eiji 6 2014 Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109Poláčik, P.; Terracini, Susanna 4 2014 On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034Poláčik, Peter 4 2014 Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109Poláčik, Peter; Yanagida, Eiji 3 2014 The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127Du, Yihong; Peng, Rui; Poláçik, Peter 7 2012 On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073Poláčik, P. 5 2012 Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074Poláčik, P. 2 2012 On asymptotically symmetric parabolic equations. Zbl 1262.35041Földes, Juraj; Poláčik, Peter 1 2012 Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\). Zbl 1262.35130Poláčik, P. 20 2011 Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol 20 2011 Convergence to a steady state for asymptotically autonomous semilinear heat equations on \(\mathbb R^N\). Zbl 1263.35035Földes, Juraj; Poláčik, P. 8 2011 Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083Poláčik, P. 5 2011 On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098Földes, J.; Poláčik, Peter 22 2009 Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042Poláčik, P. 10 2009 Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150Poláčik, Peter; Yanagida, Eiji 3 2009 Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153Poláčik, P.; Šverák, V. 6 2008 Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\). Zbl 1170.35021Húska, Juraj; Poláčik, Peter 4 2008 Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014Poláčik, Peter; Quittner, Pavol 3 2008 Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 150 2007 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 57 2007 Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V. 17 2007 Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063Poláčik, Peter 10 2007 Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011Lou, Yuan; Martínez, Salomé; Poláčik, Peter 22 2006 A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045Poláčik, Peter; Quittner, Pavol 22 2006 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). II: Entire solutions. Zbl 1128.35051Poláčik, P. 7 2006 A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044Poláčik, P.; Yanagida, E. 19 2005 Immediate regularization after blow-up. Zbl 1102.35053Fila, Marek; Matano, Hiroshi; Polácik, Peter 18 2005 Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037Poláčik, Peter; Quittner, Pavol 8 2005 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045Poláčik, P. 8 2005 On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030Poláčik, P. 8 2005 Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391Húska, J.; Poláčik, P.; Safonov, M. V. 3 2005 Immediate regularization after blow-up. Zbl 1108.35092Fila, M.; Matano, H.; Poláčik, P. 3 2005 The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353Húska, Juraj; Poláčik, Peter 11 2004 Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403Poláčik, P.; Yanagida, E. 7 2004 On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055Poláčik, Peter; Yanagida, Eiji 60 2003 Competing species near a degenerate limit. Zbl 1043.35080Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P. 32 2003 Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045Jendoubi, M. A.; Poláčik, P. 8 2003 Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001Poláčik, P. 27 2002 Convergence to equilibrium for semilinear parabolic problems in \(\mathbb{R}^N\). Zbl 1021.35013Busca, J.; Jendoubi, M. A.; Poláčik, P. 25 2002 Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046Poláčik, P.; Simondon, F. 17 2002 Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054Fila, Marek; Matano, Hiroshi; Poláčik, Peter 5 2002 Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009Poláčik, P. 2 2002 Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051Poláčik, Peter; Yanagida, Eiji 2 2002 The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035Hutson, V.; Mischaikow, K.; Poláčik, P. 79 2001 Monotonicity of stable solutions in shadow systems. Zbl 0981.35018Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji 19 2001 Morse indices and bifurcations of positive solutions of \(\Delta u+f(u)=0\) on \(\mathbb R^ N\). Zbl 1101.35321Poláčik, Peter 6 2001 Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023Poláčik, Peter; Yanagida, Eiji 3 2001 Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on \(\mathbb{R}\). Zbl 0987.35079Feireisl, Eduard; Poláčik, Peter 17 2000 Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060Dancer, E. N.; Poláčik, P. 9 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 Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097Poláčik, Peter 1 1999 The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062Brunovský, P.; Poláčik, P. 28 1997 On the local structure of \(\omega\)-limit sets of maps. Zbl 0889.34048Brunovský, P.; Poláčik, P. 12 1997 Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059Chen, Xu-Yan; Poláčik, Peter 33 1996 Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054Poláčik, Peter; Rybakowski, Krzysztof P. 30 1996 Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065Poláčik, Peter; Šošovička, Vladimír 4 1996 High-dimensional \(\omega\)-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060Poláčik, Peter 10 1995 Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073Chen, Xu-Yan; Poláčik, Peter 7 1995 Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074Poláčik, Peter; Rybakowski, Krzysztof 5 1995 Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049Hess, Peter; Poláčik, P. 19 1994 Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008Poláčik, P.; Tereščák, I. 14 1994 Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041Poláčik, Peter 6 1994 Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065Poláčik, Peter 2 1994 Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002Poláčik, P.; Tereščák, Ignác 44 1993 Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077Hess, Peter; Poláčik, Peter 15 1993 Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009Brunovský, P.; Poláčik, P.; Sandstede, B. 26 1992 Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011Haraux, A.; Poláčik, P. 17 1992 Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046Poláčik, P. 7 1992 Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039Poláčik, P.; Tereščák, I. 48 1991 Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027Poláčik, Peter 17 1991 Realization of any finite jet in a scalar semilinear parabolic equation on the ball in \(\mathbb{R}^ 3\). Zbl 0774.35041Poláčik, Peter 9 1991 Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J. 4 1991 Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060Fiedler, Bernold; Poláčik, Peter 31 1990 Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054Poláčik, Peter 2 1990 Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043Poláčik, P. 2 1990 Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064Poláčik, Peter 40 1989 Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036Poláčik, Peter 7 1989 Group actions on strongly monotone dynamical systems. Zbl 0642.58031Mierczyński, Janusz; Poláčik, Peter 5 1989 Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions. Zbl 0639.35039Poláčik, Peter 6 1987 Generic hyperbolicity for reaction diffusion equations on symmetric domains. Zbl 0622.35005Brunovský, Pavol; Poláčik, Peter 4 1987 all cited Publications top 5 cited Publications all top 5 Cited by 833 Authors 47 Poláčik, Peter 25 Lou, Yuan 17 Yanagida, Eiji 14 Shen, Wenxian 13 Fila, Marek 13 Winkler, Michael 12 Matano, Hiroshi 11 Du, Yihong 11 Mizoguchi, Noriko 11 Souplet, Philippe 11 Wang, Yi 11 Wei, Juncheng 10 Li, Wan-Tong 10 Lou, Bendong 10 Mierczyński, Janusz 10 Obaya, Rafael 10 Peng, Rui 10 Phan, Quoc Hung 10 Weth, Tobias 9 Ishige, Kazuhiro 8 Jendoubi, Mohamed Ali 8 Jiang, Jifa 8 Quittner, Pavol 8 Sanz, Ana M. 8 Villavert, John 8 Wang, Zhi Cheng 8 Yi, Taishan 8 Zhao, Xiao-Qiang 8 Zou, Wenming 7 Chill, Ralph 7 Guo, Zongming 7 Smith, Hal Leslie 7 Vishnevskii, Mikhail P. 6 Cosner, Chris 6 Földes, Juraj 6 Shi, Junping 6 Wu, Jianhua 6 Zhou, Maolin 5 Dancer, Edward Norman 5 Duong, Anh Tuan 5 Fiedler, Bernold 5 Giga, Yoshikazu 5 Giletti, Thomas 5 Harrabi, Abdellaziz 5 Jänig, Axel 5 Kawakami, Tatsuki 5 Langa, Jose’ Antonio 5 Nadin, Grégoire 5 Rodríguez-Bernal, Aníbal 5 Ruan, Shigui 5 Vazquez, Juan Luis 5 Wang, Mingxin 5 Wu, Hao 5 Yang, Hui 4 Cantrell, Robert Stephen 4 Cholewa, Jan W. 4 Ducrot, Arnaud 4 Dupaigne, Louis 4 Fujishima, Yohei 4 García-Melián, Jorge 4 Grasselli, Maurizio 4 Hamel, François 4 Húska, Juraj 4 Joly, Romain 4 Lam, King-Yeung 4 Li, Congming 4 Miyamoto, Yasuhito 4 Naito, Yūki 4 Nolasco de Carvalho, Alexandre 4 Rocha, Carlos 4 Roquejoffre, Jean-Michel 4 Saldaña, Alberto 4 Vakulenko, Sergey A. 4 Vétois, Jérôme 4 Wan, FangShu 4 Wang, Yuxia 4 Wu, Jianhong 4 Zheng, Gao-Feng 4 Zheng, Songmu 3 Alfaro, Matthieu 3 Arrieta, José M. 3 Bao, Jiguang 3 Berestycki, Henri 3 Brunovský, Pavol 3 Chen, Xinfu 3 Cheng, Ze 3 Cortázar, Carmen 3 Dávila, Juan 3 Del Pino, Manuel A. 3 Ding, Weiwei 3 Dlotko, Tomasz W. 3 Enciso, Germán Andrés 3 Farina, Alberto 3 Feireisl, Eduard 3 Feng, Lirui 3 Freitas, Pedro 3 Guo, Jong-Shenq 3 Gyllenberg, Mats 3 Hirata, Kentaro 3 Hirsch, Morris W. ...and 733 more Authors all top 5 Cited in 136 Serials 135 Journal of Differential Equations 46 Journal of Dynamics and Differential Equations 44 Journal of Mathematical Analysis and Applications 42 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 26 Discrete and Continuous Dynamical Systems 24 Calculus of Variations and Partial Differential Equations 19 Journal of Functional Analysis 17 Journal of Mathematical Biology 16 Transactions of the American Mathematical Society 15 Communications on Pure and Applied Analysis 14 Mathematische Annalen 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 Nonlinear Analysis. Real World Applications 13 Proceedings of the American Mathematical Society 13 Discrete and Continuous Dynamical Systems. Series B 12 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 12 Communications in Contemporary Mathematics 11 Communications in Partial Differential Equations 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 NoDEA. Nonlinear Differential Equations and Applications 10 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Archive for Rational Mechanics and Analysis 9 Advances in Mathematics 9 Journal of Evolution Equations 8 Nonlinearity 8 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Advances in Difference Equations 6 Siberian Mathematical Journal 6 SIAM Journal on Mathematical Analysis 5 Applicable Analysis 5 Bulletin of Mathematical Biology 5 Applied Mathematics Letters 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 Advances in Nonlinear Analysis 3 Communications in Mathematical Physics 3 Rocky Mountain Journal of Mathematics 3 Archiv der Mathematik 3 Journal of Computational and Applied Mathematics 3 Physica D 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Journal of Nonlinear Science 3 Advanced Nonlinear Studies 3 Milan Journal of Mathematics 3 Mathematical Biosciences and Engineering 3 Boundary Value Problems 3 Complex Variables and Elliptic Equations 3 Journal of Fixed Point Theory and Applications 3 Discrete and Continuous Dynamical Systems. Series S 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 Chaos, Solitons and Fractals 2 Acta Mathematica 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 Journal of Integral Equations and Applications 2 Topological Methods in Nonlinear Analysis 2 Electronic Journal of Differential Equations (EJDE) 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Revista Matemática Complutense 2 Journal of the European Mathematical Society (JEMS) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Proceedings of the Steklov Institute of Mathematics 2 Analysis and Mathematical Physics 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 Applied Mathematics and Computation 1 Automatica 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 Journal of the Korean Mathematical Society 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik 1 Mathematica Slovaca 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Studies in Applied Mathematics 1 Theoretical Population Biology 1 Ergodic Theory and Dynamical Systems 1 Zeitschrift für Analysis und ihre Anwendungen 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Annals of Pure and Applied Logic 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations ...and 36 more Serials all top 5 Cited in 29 Fields 670 Partial differential equations (35-XX) 153 Biology and other natural sciences (92-XX) 130 Dynamical systems and ergodic theory (37-XX) 71 Ordinary differential equations (34-XX) 32 Operator theory (47-XX) 22 Integral equations (45-XX) 22 Global analysis, analysis on manifolds (58-XX) 10 Fluid mechanics (76-XX) 8 Difference and functional equations (39-XX) 8 Functional analysis (46-XX) 8 Numerical analysis (65-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Probability theory and stochastic processes (60-XX) 6 Potential theory (31-XX) 6 Differential geometry (53-XX) 6 General topology (54-XX) 6 Statistical mechanics, structure of matter (82-XX) 6 Systems theory; control (93-XX) 5 Mechanics of particles and systems (70-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Real functions (26-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) 1 Combinatorics (05-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) Citations by Year