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

Zejia Wang; Suzhen Xu; Huijuan Song

doi:10.3934/dcdsb.2018129

Article Contents

2018, Volume 23, Issue 6: 2593-2605. Doi: 10.3934/dcdsb.2018129

This issue Previous Article The modified Camassa-Holm equation in Lagrangian coordinates Next Article Fink type conjecture on affine-periodic solutions and Levinson's conjecture to Newtonian systems

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
* Corresponding author: Huijuan Song

Received: July 2017

Revised: October 2017

Early access: July 2018

Published: June 2018

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B35, 35K35; Secondary: 35Q80.

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