| Abstract: | 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 factthat the maximum principle does not hold for the CH equation. Therefore, a generalized CH equation with logistic source may cause the negative concentration blow-upproblem in finite time. To overcome this drawback, we propose the cut-off logisticsource such that only the positive value greater than a given critical concentrationcan 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. Numericalsolutions are obtained using a finite difference multigrid solver. Moreover, we perform numerical tests for tumor growth simulation, which is a typical application ofgeneralized CH equations in biology. We apply the proposed cut-off logistic sourceterm and have good results. |
