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

Jiayue Zheng; Shangbin Cui

doi:10.3934/dcdsb.2020103

Article Contents

2020, Volume 25, Issue 11: 4397-4410. Doi: 10.3934/dcdsb.2020103

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

Jiayue Zheng and
Shangbin Cui^,

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

^* Corresponding author: Shangbin Cui
^* Corresponding author: Shangbin Cui

Received: October 2011

Early access: April 2020

Published: November 2020

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

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Abstract

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.

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Mathematics Subject Classification: 35R35; 46N60; 92B99.

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