Long-time dynamics of the parabolic $p$-Laplacian equation

TL;DR

This paper investigates the long-term behavior of solutions to the parabolic p-Laplacian equation with variable coefficients, establishing the existence of a compact global attractor in L^2(R^n).

Contribution

It proves the existence of a compact, invariant global attractor for the parabolic p-Laplacian with variable coefficients without requiring upper growth restrictions.

Findings

Existence of a global attractor in L^2(R^n)

Attractor is compact and invariant

Results hold under mild coefficient conditions

Abstract

In this paper, we study the long-time behaviour of solutions of Cauchy problem for the parabolic $p$-Laplacian equation with variable coefficients. Under mild conditions on the coefficient of the principal part and without upper growth restriction on the source function, we prove that this problem possesses a compact and invariant global attractor in $L^{2}(R^{n})$.