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