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Asymptotic symmetry for a class of quasi-linear parabolic problems. (English) Zbl 1253.35009

Summary: We study the symmetry properties of the weak positive solutions to a class of quasillinear elliptic problems having a variational structure. On this basis, the asymptotic behaviour of global solutions of the corresponding parabolic equations is also investigated. In particular, if the domain is a ball, the elements of the \(\omega\) limit set are nonnegative radially symmetric solutions of the stationary problem.

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
35B09 Positive solutions to PDEs
35J20 Variational methods for second-order elliptic equations
35K20 Initial-boundary value problems for second-order parabolic equations
35J25 Boundary value problems for second-order elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35K92 Quasilinear parabolic equations with \(p\)-Laplacian
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