Asymptotic Symmetry for a Class of Quasi-Linear Parabolic Problems

Advanced Nonlinear Studies - Tập 10 Số 4 - Trang 789-818 - 2010
Luigi Montoro1, Berardino Sciunzi1, Marco Squassina2
1Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31B, I-87036 Arcavacata di Rende, Cosenza, Italy
2Dipartimento di Informatica Università di Verona, Cá Vignal 2, Strada Le Grazie 15, I-37134 Verona, Italy

Tóm tắt

Abstract We study the symmetry properties of the weak positive solutions to a class of quasi-linear 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 ω limit set are nonnegative radially symmetric solutions of the stationary problem.

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