Symmetry Properties of Positive Solutions of Parabolic Equations on ℝN: I. Asymptotic Symmetry for the Cauchy Problem

DOI10.1080/03605300500299919zbMath1083.35045OpenAlexW1984822985MaRDI QIDQ5713472

Peter Poláčik

Publication date: 14 December 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300500299919

zbMATH Keywords

quasilinear parabolic equationspositive bounded solutionsradial symmetrymoving hyperplane

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Invariance and symmetry properties for PDEs on manifolds (58J70) Initial value problems for second-order parabolic equations (35K15)

Related Items

Group actions on monotone skew-product semiflows with applications, Ancient solutions to nonlocal parabolic equations, Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations, Asymptotic monotonicity of positive solutions for fractional parabolic equation on the right half space, Symmetry properties of sign-changing solutions to nonlinear parabolic equations in unbounded domains, The trichotomy of solutions and the description of threshold solutions for periodic parabolic equations in cylinders, Stability of the phase separation state for compressible Navier-Stokes/Allen-Cahn system, Monotonicity and one-dimensional symmetry of solutions for fractional reaction-diffusion equations and various applications of sliding methods, Symmetry of positive solutions of asymptotically symmetric parabolic problems on \(\mathbb R^N\), Asymptotic symmetry for a class of nonlinear fractional reaction-diffusion equations, Asymptotic method of moving planes for fractional parabolic equations, SYMMETRY AND MONOTONICITY OF SOLUTIONS TO FRACTIONAL ELLIPTIC AND PARABOLIC EQUATIONS, Uniqueness of limit flow for a class of quasi-linear parabolic equations, Asymptotic axial symmetry of solutions of parabolic equations in bounded radial domains, Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\), Symmetry Properties of Positive Solutions of Parabolic Equations on ℝ^N: II. Entire Solutions, Navier-Stokes/Allen-Cahn system with generalized Navier boundary condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A characteristic property of spheres
• Symmetry and related properties via the maximum principle
• Symmetry properties in systems of semilinear elliptic equations
• Symmetrization properties of parabolic equations in symmetric domains
• The symmetry of positive solutions of periodic-parabolic problems
• Long-time behavior and convergence for semilinear wave equations on \(\mathbb{R}^ N\)
• Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders
• On bounded and unbounded global solutions of a supercritical semilinear heat equation
• Symmetry results for semilinear elliptic systems in the whole space
• Continuous rearrangement and symmetry of solutions of elliptic problems
• One-dimensional symmetry of bounded entire solutions of some elliptic equations
• Symmetry of ground states of quasilinear elliptic equations
• Symmetry of instabilities for scalar equations in symmetric domains
• Attractors of non-autonomous parabolic equations and their symmetry properties
• A symmetry problem in potential theory
• Monotonicity of stable solutions in shadow systems
• Radial symmetry of positive solutions of nonlinear elliptic equations in Rⁿ
• Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains
• Some notes on the method of moving planes
• On the stability and instability of positive steady states of a semilinear heat equation in ℝn
• Stability analysis in order-preserving systems in the presence of symmetry
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Symmetry and convergence properties for non-negative solutions of nonautonomous reaction–diffusion problems
• Monotonicity and Symmetry of Solutions of Fully Nonlinear Elliptic Equations on Bounded domains
• The problem of uniqueness of the limit in a semilinear heat equation
• CONVERGENCE TO EQUILIBRIUM FOR SEMILINEAR PARABOLIC PROBLEMS IN
• On the method of moving planes and the sliding method
• Further study on a nonlinear heat equation