JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 卷:399 |
A two-phase free boundary problem with discontinuous velocity: Application to tumor model | |
Article | |
Chen, Duan1  Friedman, Avner1,2  | |
[1] Ohio State Univ, Math Biosci Inst, Columbus, OH 43210 USA | |
[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA | |
关键词: Free boundary problem; Tumor growth; Existence and uniqueness; | |
DOI : 10.1016/j.jmaa.2012.10.035 | |
来源: Elsevier | |
【 摘 要 】
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 Omega(t) is enclosed by the free boundary Gamma(t), and the exterior of the tumor, D(t), consists of a healthy normal tissue. Due to cancer cell proliferation, the convective velocity (v) over right arrow of cells is discontinuous across the free boundary; the motion of the free boundary Gamma(t) is determined by (v) over right arrow. We prove the existence and uniqueness of a solution to this system in the radially symmetric case for a small time interval 0 <= t <= T, and apply the analysis to the full tumor growth model. Published by Elsevier Inc.
【 授权许可】
Free
【 预 览 】
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10_1016_j_jmaa_2012_10_035.pdf | 299KB | download |