Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2022; 37(2): 423-443

Online first article March 29, 2022      Printed April 30, 2022

https://doi.org/10.4134/CKMS.c210061

Copyright © The Korean Mathematical Society.

Global attractor for a semilinear strongly degenerate parabolic equation with exponential nonlinearity in unbounded domains

Nguyen Xuan Tu

Hung Vuong university

Abstract

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on $mathbb R^N $. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic {it a priori} estimate method.

Keywords: Degenerate parabolic equation, exponential nonlinearity, unbounded domain, weak solution, global attractor

MSC numbers: 35B41, 35D30, 37K65

Supported by: This research is funded by Hung Vuong University.