Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7221926 | Nonlinear Analysis: Real World Applications | 2018 | 20 Pages |
Abstract
This paper is concerned with a free boundary problem modeling the growth of solid tumor spheroid with angiogenesis. The model comprises a coupled system of two elliptic equations describing the distribution of nutrient concentration Ï
and inner pressure p within the tumor tissue. Angiogenesis results in a new boundary condition ânÏ+βÏâϯ=0 instead of the widely studied condition Ï=ϯ over the moving boundary, where β is a positive constant. We first prove that this problem admits a unique radial stationary solution, and this solution is globally asymptotically stable under radial perturbations. Then we establish local well-posedness of the problem and study asymptotic stability of the radial stationary solution under non-radial perturbations. A positive threshold value γâ is obtained such that the radial stationary solution is asymptotically stable for γ>γâ
and unstable for 0<γ<γâ.
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Authors
Yuehong Zhuang,