Symmetrization properties of parabolic equations in symmetric domains

DOI10.1007/BF02218852zbMath0807.35065MaRDI QIDQ1340466

Anatoli V. Babin

Publication date: 19 December 1994

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemsymmetric domainasymptotical symmetrization propertysymmetry properties of positive solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Initial-boundary value problems for higher-order parabolic equations (35K35) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (10)

A symmetry property for fully nonlinear elliptic equations on the sphere ⋮ Qualitative properties of coexistence and semi-trivial limit profiles of nonautonomous nonlinear parabolic Dirichlet systems ⋮ Symmetry of positive solutions of asymptotically symmetric parabolic problems on \(\mathbb R^N\) ⋮ Attractors of non-autonomous parabolic equations and their symmetry properties ⋮ SYMMETRY AND MONOTONICITY OF SOLUTIONS TO FRACTIONAL ELLIPTIC AND PARABOLIC EQUATIONS ⋮ Symmetry Properties of Positive Solutions of Parabolic Equations on ℝ^N: I. Asymptotic Symmetry for the Cauchy Problem ⋮ Equilibria with a nontrivial nodal set and the dynamics of parabolic equations on symmetric domains ⋮ On symmetry properties of parabolic equations in bounded domains ⋮ Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains ⋮ Symmetry Properties of Positive Solutions of Parabolic Equations on ℝ^N: II. Entire Solutions

Cites Work

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• Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
• The Morse-Smale property for a semilinear parabolic equation
• Symmetry-breaking for positive solutions of semilinear elliptic equations
• Symmetry and related properties via the maximum principle
• Attractors of non-autonomous parabolic equations and their symmetry properties
• A symmetry problem in potential theory
• On Non-Radially Symmetric Bifurcation
• On the method of moving planes and the sliding method
• Symmetry breaking for a class of semilinear elliptic problems

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