# American Institute of Mathematical Sciences

August  2018, 23(6): 2593-2605. doi: 10.3934/dcdsb.2018129

## Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor

 College of Mathematical and Informational Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

* Corresponding author: Huijuan Song

Received  July 2017 Revised  October 2017 Published  July 2018

We consider a free boundary problem modeling the growth of angiogenesis tumor with inhibitor, in which the tumor aggressiveness is modeled by a parameter $μ$. The existences of radially symmetric stationary solution and symmetry-breaking stationary solution are established. In addition, it is proved that there exist a positive integer $m^{**}$ and a sequence of $μ_m$, such that for each $μ_m(m > m^{**})$, the symmetry-breaking stationary solution is a bifurcation branch of the radially symmetric stationary solution.

Citation: Zejia Wang, Suzhen Xu, Huijuan Song. Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2593-2605. doi: 10.3934/dcdsb.2018129
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