期刊论文详细信息
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
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【 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】

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