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