Examining age-specific heterogeneity of susceptibility to cardiovascular disease is also essential in individuals without prediabetes to determine its relative size and direction compared to those with prediabetes.Of ...Examining age-specific heterogeneity of susceptibility to cardiovascular disease is also essential in individuals without prediabetes to determine its relative size and direction compared to those with prediabetes.Of particular interest,age-specific heterogeneity in genetic susceptibility may exhibit opposite directions depending on the presence or absence of prediabetes.展开更多
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Supported by National Research Foundation of Korea,No.2018R1A2B6004867.
文摘Examining age-specific heterogeneity of susceptibility to cardiovascular disease is also essential in individuals without prediabetes to determine its relative size and direction compared to those with prediabetes.Of particular interest,age-specific heterogeneity in genetic susceptibility may exhibit opposite directions depending on the presence or absence of prediabetes.
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.
