This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow’s model [16] discussed in [8, 9]modeling a proliferating age structured cell pop...This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow’s model [16] discussed in [8, 9]modeling a proliferating age structured cell population with inherited properties. We give existence and uniqueness results on appropriate weighted L~p-spaces with 1 ≤ p < ∞ in the case where the rate of cells mortality σ and the transition rate k are depending on the total density of population. General local and nonlocal reproduction rules are considered.展开更多
We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We il...We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We illustrate numerically the efficiency of the approach and compare it with several variants of MsFEM.展开更多
文摘This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow’s model [16] discussed in [8, 9]modeling a proliferating age structured cell population with inherited properties. We give existence and uniqueness results on appropriate weighted L~p-spaces with 1 ≤ p < ∞ in the case where the rate of cells mortality σ and the transition rate k are depending on the total density of population. General local and nonlocal reproduction rules are considered.
基金supported by ONR under Grant (No. N00014-12-1-0383)EOARD under Grant (No. FA8655-10-C-4002)
文摘We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We illustrate numerically the efficiency of the approach and compare it with several variants of MsFEM.
