EXISTENCE AND LONG-TIME BEHAVIOR OF SOLUTIONS TO A CLASS OF DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING WEIGHTED p-LAPLACIAN OPERATORS

DOI: 10.18173/2354-1059.2025-0019

Abstract

In this paper, we study the existence, uniqueness, and long-time behavior of global weak solutions to a class of doubly nonlinear degenerate parabolic equations involving weighted p-Laplacian operators in bounded domains with homogeneous Dirichlet boundary conditions. The global existence and uniqueness of weak solutions are established by combining compactness arguments with the theory of monotone operators. Furthermore, we analyze the asymptotic dynamics of the system and prove the existence of a compact global attractor by employing the theory of global attractors in bi-spaces.