Global attractor for a class of quasilinear degenerate parabolic equations with nonlinearity of arbitrary order
Commun. Korean Math. Soc.
Published online May 12, 2021
Tran Thi Quynh Chi, Le Thi Thuy, and Nguyen Xuan Tu
Department of Mathematics, Electric Power University, Hung Vuong University
Abstract : In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted $p$-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic {\it a priori} estimates method.
Keywords : Quasilinear degenerate parabolic equation; Weighted p-Laplacian operator; Weak solution; Global attractor; Compactness method; Monotonicity method; Weak convergence techniques; Orlicz spac
MSC numbers : 35B41; 35K65; 35D05.
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