Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2021; 36(3): 447-463

Online first article May 12, 2021      Printed July 31, 2021

https://doi.org/10.4134/CKMS.c190332

Copyright © The Korean Mathematical Society.

Global attractor for a class of quasilinear degenerate parabolic equations with nonlinearity of arbitrary order

Tran Thi Quynh Chi, Le Thi Thuy, Nguyen Xuan Tu

Electric Power University; Electric Power University; Hung Vuong university

Abstract

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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 spaces, asymptotic a priori estimate method

MSC numbers: 35B41, 35K65, 35D05

Supported by: The research of the third author is supported by the Hung Vuong University.

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