Existence and Blow-up of Smooth Solutions for Cahn-Hilliard Equation with Inertial Term

作     者：DING Rong WU Zhigang 丁蓉;吴志刚

作者机构：College of Science Donghua University 

出 版 物：《Journal of Donghua University(English Edition)》 (东华大学学报（英文版）)

年 卷 期：2019年第36卷第4期

页      面：413-420页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Natural Science Foundation of China(No.11971100) Fundamental Research Funds for the Central Universities,China(No.2232019D3-43) 

主　　题：Cahn-Hilliard equation with inertial term existence blow-up 

摘      要：The motivation of this paper is to systematically study how the inertial term affects the behavior of the solution of the Cahn-Hilliard *** there is an inertial term,the equation becomes a parabolic-hyperbolic *** overcome the difficulties from large perturbation and the hyperbolicity,a few elaborate energy estimates should be given,which are based on choosing suitable space of the smooth solution,even some inequalites in negative Sobolev *** precisely,for 1-dimensional(1D)non-viscous case and 1D,2D,and 3D viscous case,the global existence of the smooth solutions are ***,several blow-up results are established by using the convex *** results exhibit the interplay between the viscosity and the inertial term for the behavior of the smooth solution.