# American Institute of Mathematical Sciences

## Bifurcation analysis of a tumor-model free boundary problem with a nonlinear boundary condition

 School of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China

* Corresponding author: Shangbin Cui

Received  October 2011 Published  April 2020

Fund Project: This work is supported by China National Natural Science Foundation under the grant number 11571381

In this paper we study existence of nonradial stationary solutions of a free boundary problem modeling the growth of nonnecrotic tumors. Unlike the models studied in existing literatures on this topic where boundary value condition for the nutrient concentration $\sigma$ is linear, in this model this is a nonlinear boundary condition. By using the bifurcation method, we prove that nonradial stationary solutions do exist when the surface tension coefficient $\gamma$ takes values in small neighborhoods of certain eigenvalues of the linearized problem at the radial stationary solution.

Citation: Jiayue Zheng, Shangbin Cui. Bifurcation analysis of a tumor-model free boundary problem with a nonlinear boundary condition. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020103
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