Skip to content Skip to navigation

Attractors for a Semilinear Parabolic System Involving the Grushin Operator

Volume 3, Number 2 (2012), 1 - 16

Attractors for a Semilinear Parabolic System Involving the Grushin Operator

Communicated By: 
Alain Haraux
Price: $20.00

Abstract

Considered here is the first initial boundary value problem for a semilinear degenerate
parabolic system involving the Grushin operator. We prove the existence of a finite-dimensional
global attractor in (L2(
))m for the semigroup associated to the problem in the general case. When
the system has a gradient structure, the global attractor is shown to be more regular by using the
so-called asymptotic a priori estimate method.