Existence and regularity of a global attractor for doubly nonlinear parabolic equations

Abstract

In this paper we consider a doubly nonlinear parabolic partial differential equation $$ frac{partial eta (u)}{partial t}-Delta _{p}u+f(x,t,u)=0 quad hbox{in }Omega imesmathbb{R}^{+}, $$ with Dirichlet boundary condition and initial data given. We prove the existence of a global compact attractor by using a dynamical system approach. Under additional conditions on the nonlinearities $Beta$, $f$, and on $p$, we prove more regularity for the global attractor and obtain stabilization results for the solutions.

Keywords

• p-Laplacian
• a-priori estimate
• long time behaviour
• dynamical system
• absorbing set
• global attractor.