# American Institute of Mathematical Sciences

August  2008, 21(3): 929-943. doi: 10.3934/dcds.2008.21.929

## Well-posedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord

 1 Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China 2 Institute of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China

Received  June 2007 Revised  December 2007 Published  April 2008

In this paper we study a multidimensional moving boundary problem modeling the growth of tumor cord. This problem contains two coupled elliptic equations defined in a bounded domain in $R^2$ whose boundary consists of two disjoint closed curves, one fixed and the other moving and a priori unknown. The evolution of the moving boundary is governed by a Stefan type equation. By using the functional analysis method based on applications of the theory of analytic semigroups, we prove that (1) this problem is locally well-posed in Hölder spaces, (2) it has a unique radially symmetric stationary solution, and (3) this radially symmetric stationary solution is asymptotically stable for arbitrary sufficiently small perturbations in these Hölder spaces.
Citation: Fujun Zhou, Shangbin Cui. Well-posedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. Discrete & Continuous Dynamical Systems, 2008, 21 (3) : 929-943. doi: 10.3934/dcds.2008.21.929
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