Asymptotic behavior of solutions of a free boundary problem
modelling the growth of tumors with Stokes equations
Junde Wu - Department of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China (email)
Abstract: We study a free boundary problem modelling the growth of non-necrotic tumors with fluid-like tissues. The fluid velocity satisfies Stokes equations with a source determined by the proliferation rate of tumor cells which depends on the concentration of nutrients, subject to a boundary condition with stress tensor effected by surface tension. It is easy to prove that this problem has a unique radially symmetric stationary solution. By using a functional approach, we prove that there exists a threshold value γ* > 0 for the surface tension coefficient $\gamma$, such that in the case γ > γ* this radially symmetric stationary solution is asymptotically stable under small non-radial perturbations, whereas in the opposite case it is unstable.
Keywords: Free boundary problem, tumor growth,
Stokes equations, stationary solution, asymptotic stability.
Received: July 2008; Revised: November 2008; Published: March 2009.
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