American Institute of Mathematical Sciences

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September  2009, 8(5): 1669-1688. doi: 10.3934/cpaa.2009.8.1669

Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of multi-layer tumors

Fujun Zhou 1, , Junde Wu 2, and  Shangbin Cui 2,

1. 

Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640
2. 

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

Received  August 2008 Revised  January 2009 Published  April 2009

In this paper we study a moving boundary problem modeling the growth of multi-layer tumors under the action of inhibitors. The problem contains two coupled reaction-diffusion equations and one elliptic equation defined on a strip-like domain in $R^n$, with one part of the boundary moving and a priori unknown. The evolution of the moving boundary is governed by a Stefan type equation, with the surface tension effect taken into consideration. Local existence and asymptotic behavior of solutions to this problem are investigated. The analysis is based on the employment of the functional analysis method combing with the well-posedness and geometric theory for parabolic differential equations in Banach spaces.
Keywords: Moving boundary problem, multi-layer tumors, asymptotic behavior..
Mathematics Subject Classification: Primary: 35R35, 35B35; Secondary: 76D2.
Citation: Fujun Zhou, Junde Wu, Shangbin Cui. Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of multi-layer tumors. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1669-1688. doi: 10.3934/cpaa.2009.8.1669
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