Finite Element Variational Crimes in Parabolic-Elliptic Problems. Part I. Nonlinear Schemes.
Free Boundary Problems Associated with Multiscale Tumor Models
The present paper introduces a tumor model with two time scales, the time t during which the tumor grows and the cycle time of individual cells. The model also includes the effects of gene mutations on the population density of the tumor cells. The model is formulated as a free boundary problem for a coupled system of elliptic, parabolic and hyperbolic equations within the tumor region, with nonlinear and nonlocal terms. Existence and uniqueness theorems are proved, and properties of the free boundary...