World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
30
Citations
3425
World Ranking
3546
National Ranking
1368

Research.com Recognitions

  • 2018 - Fellow of the American Mathematical Society For contributions to analysis of partial differential equations and infinite-dimensional dynamical systems.

Overview

Peter Poláčik is affiliated with the University of Minnesota in the United States. Their research primarily spans the fields of Mathematics and Computer Science, with a particular focus on applied mathematics and computational theory. Their work addresses various aspects of nonlinear partial differential equations and advanced mathematical modeling in engineering.

The researcher's body of work encompasses multiple subfields including applied mathematics, computational theory and mathematics, control and systems engineering, public health, environmental and occupational health, and statistical and nonlinear physics.

Main research topics covered in their publications include:

  • Advanced Mathematical Modeling in Engineering
  • Nonlinear Partial Differential Equations
  • Stability and Controllability of Differential Equations
  • Nonlinear Differential Equations Analysis
  • Mathematical and Theoretical Epidemiology and Ecology Models
  • Quantum chaos and dynamical systems
  • Geometric Analysis and Curvature Flows

Frequent collaborators in their work include Antoine Pauthier, Darío A. Valdebenito, Pavol Quíttner, Chiun-Chuan Chen, and Yuan Lou.

Publications by Peter Poláčik have appeared in a range of academic venues. Notable venues where multiple works have been published include:

  • arXiv (Cornell University)
  • Discrete and Continuous Dynamical Systems
  • Journal of Dynamics and Differential Equations
  • Memoirs of the American Mathematical Society
  • Proceedings of the American Mathematical Society

Significant recent papers authored by Peter Poláčik are:

  • "Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on ℝ," 2020, Memoirs of the American Mathematical Society
  • "Entire solutions and a Liouville theorem for a class of parabolic equations on the real line," 2020, Proceedings of the American Mathematical Society
  • "Large-time behavior of solutions of parabolic equations on the real line with convergent initial data III: unstable limit at infinity," 2022, Partial Differential Equations and Applications
  • "Further results on quasiperiodic partially localized solutions of homogeneous elliptic equations on ℝN+1," 2022, Journal of Functional Analysis
  • "Nonexistence of radial time-periodic solutions of reaction-diffusion equations with generic nonlinearities," 2023, Journal of Differential Equations

In 2018, Peter Poláčik was named a Fellow of the American Mathematical Society for contributions to the analysis of partial differential equations and infinite-dimensional dynamical systems.

Best Publications

  • Singularity and decay estimates in superlinear problems via Liouville-type theorems, I: Elliptic equations and systems

    Peter Poláčik;Pavol Quittner;Philippe Souplet

  • The evolution of dispersal rates in a heterogeneous time-periodic environment

    V. Hutson;Konstantin Mischaikow;P. Poláčik

  • Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems

    P. Poláčik;I. Tereščák

  • Singularity and decay estimates in superlinear problems via liouville-type theorems. Part II: Parabolic equations

    Peter Polácik;Pavol Quittner;Philippe Souplet

  • Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations

    Peter Polacik;Ignác Tereščák

  • Chapter 16 - Parabolic Equations: Asymptotic Behavior and Dynamics on Invariant Manifolds

    P. Poláčik

  • Convergence in smooth strongly monotone flows defined by semilinear parabolic equations

    Peter Poláčik

  • Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball

    Xu Yan Chen;Peter Polácik

  • Nonconvergent Bounded Trajectories in Semilinear Heat Equations

    Peter Poláčik;Krzysztof P. Rybakowski

  • Convergence in general periodic parabolic equations in one space dimension

    P. Brunovský;P. Polác fcaron;ik;B. Sandstede

  • Threshold Solutions and Sharp Transitions for Nonautonomous Parabolic Equations on \({\mathbb{R}^N}\)

    Peter Polacik

  • Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains

    P. Poláčik;F. Simondon

  • Competing species near a degenerate limit

    Vivian Hutson;Yuan Lou;Konstantin Mischaikow;Peter Polácik

  • The Morse–Smale Structure of a Generic Reaction–Diffusion Equation in Higher Space Dimension

    P. Brunovský;P. Poláčik

  • Complicated dynamics of scalar reaction diffusion equations with a nonlocal term

    Bernold Fiedler;Peter Poláčik

  • Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems

    Peter Hess;Peter Poláčik

  • Immediate regularization after blow-up

    Marek Fila;Hiroshi Matano;Peter Polácik

  • Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations

    Juraj Húska;Peter Poláčik;Mikhail V. Safonov

  • A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation

    Peter Poláčik;Pavol Quittner

  • CONVERGENCE TO EQUILIBRIUM FOR SEMILINEAR PARABOLIC PROBLEMS IN

    J. Busca;M. A. Jendoubi;P. Poláčik

  • On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry

    J. Földes;Peter Poláčik

  • CONVERGENCE TO A POSITIVE EQUILIBRIUM FOR SOME NONLINEAR EVOLUTION EQUATIONS IN A BALL

    Unknown

Frequent Co-Authors

Yuan Lou
Yuan Lou Shanghai Jiao Tong University
Yihong Du
Yihong Du University of New England
Vladimír Šverák
Vladimír Šverák University of Minnesota
Philippe Souplet
Philippe Souplet Paris 13 University
Konstantin Mischaikow
Konstantin Mischaikow Rutgers, The State University of New Jersey
Thomas Bartsch
Thomas Bartsch University of Giessen
Susanna Terracini
Susanna Terracini University of Turin
Eduard Feireisl
Eduard Feireisl Czech Academy of Sciences
Wei Ming Ni
Wei Ming Ni Chinese University of Hong Kong, Shenzhen
Bernold Fiedler
Bernold Fiedler Freie Universität Berlin

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