Bifurcation for a free boundary problem modeling the growth of necrotic multilayered tumors

Junde Wu

doi:10.3934/dcds.2019140

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2019, Volume 39, Issue 6: 3399-3411. Doi: 10.3934/dcds.2019140

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Bifurcation for a free boundary problem modeling the growth of necrotic multilayered tumors

Junde Wu

Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, China

Received: August 2018

Published: February 2019

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Abstract

In this paper we study bifurcation solutions of a free boundary problem modeling the growth of necrotic multilayered tumors. The tumor model consists of two elliptic differential equations for nutrient concentration and pressure, with discontinuous terms and two free boundaries. The novelty is that different types of boundary conditions are imposed on two free boundaries. By bifurcation analysis, we show that there exist infinitely many branches of non-flat stationary solutions bifurcating from the unique flat stationary solution.

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Mathematics Subject Classification: Primary: 35B32, 35R35; Secondary: 35Q92.

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