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Bull. Korean Math. Soc. 2015; 52(4): 1059-1068

Printed July 31, 2015

https://doi.org/10.4134/BKMS.2015.52.4.1059

Copyright © The Korean Mathematical Society.

Existence and large time behavior of solutions to a fourth-order degenerate parabolic equation

Bo Liang, Meishan Wang, and Ying Wang

Dalian Jiaotong University, Dalian Jiaotong University, Dalian Jiaotong University

Abstract

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The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.

Keywords: fourth-order parabolic, fourth-order elliptic, Cahn-Hilliard equation, thin film equation, long time behavior

MSC numbers: Primary 35G20, 35G30, 35G61, 35Q35

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