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

Montoro, Luigi; Sciunzi, Berardino; Squassina, Marco

Adv. Nonlinear Stud. 10, No. 4, 789-818 (2010).

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

Keywords:

\(\omega\) limit set; nonnegative radially symmetric solutions