Existence and large time behavior of solutions to a fourth-order degenerate parabolic equation
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1059-1068
Printed July 31, 2015
Bo Liang, Meishan Wang, and Ying Wang
Dalian Jiaotong University, Dalian Jiaotong University, Dalian Jiaotong University
Abstract : 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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