Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419200 | Journal of Mathematical Analysis and Applications | 2013 | 16 Pages |
Abstract
We consider a two-phase free boundary problem consisting of a hyperbolic equation for w and a parabolic equation for u, where w and u represent, respectively, densities of cells and cytokines in a simplified tumor growth model. The tumor region Ω(t) is enclosed by the free boundary Î(t), and the exterior of the tumor, D(t), consists of a healthy normal tissue. Due to cancer cell proliferation, the convective velocity vâ of cells is discontinuous across the free boundary; the motion of the free boundary Î(t) is determined by vâ. We prove the existence and uniqueness of a solution to this system in the radially symmetric case for a small time interval 0â¤tâ¤T, and apply the analysis to the full tumor growth model.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Duan Chen, Avner Friedman,