On the Evolutionary Dynamics of the Cahn-Hilliard Equation with Cut-Off Mass Source

作     者：Chaeyoung Lee Hyundong Kim Sungha Yoon Jintae Park Sangkwon Kim Junxiang Yang Junseok Kim 

作者机构：Department of MathematicsKorea UniversitySeoul 02841Republic of Korea 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2021年第14卷第1期

页      面：242-260页

核心收录：

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

基　　金：The first author(C.Lee)was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2019R1A6A3A13094308) The corresponding author(J.S.Kim)was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2019R1A2C1003053) 

主　　题：Cahn-Hilliard equation logistic source finite difference method tumor growth application 

摘      要：We investigate the effect of cut-off logistic source on evolutionary dynamics of a generalized Cahn-Hilliard(CH)equation in this *** is a well-known fact that the maximum principle does not hold for the CH ***,a generalized CH equation with logistic source may cause the negative concentration blow-up problem in finite *** overcome this drawback,we propose the cut-off logistic source such that only the positive value greater than a given critical concentration can *** consider the temporal profiles of numerical results in the one-,two-,and three-dimensional spaces to examine the effect of extra mass *** solutions are obtained using a finite difference multigrid ***,we perform numerical tests for tumor growth simulation,which is a typical application of generalized CH equations in *** apply the proposed cut-off logistic source term and have good results.