Analysis of a delayed free boundary problem for tumor growth

Pages: 293 - 308, Volume 15, Issue 1, January 2011

doi:10.3934/dcdsb.2011.15.293       Abstract        References        Full Text (214.4K)       Related Articles

Shihe Xu - Department of Mathematics, Zhaoqing University, Zhaoqing, 526061, China (email)

Abstract: In this paper we study a delayed free boundary problem for the growth of tumors. The establishment of the model is based on the diffusion of nutrient and mass conservation for the two process proliferation and apoptosis(cell death due to aging). It is assumed the process of proliferation is delayed compared to apoptosis. By $L^p$ theory of parabolic equations and the Banach fixed point theorem, we prove the existence and uniqueness of a local solutions and apply the continuation method to get the existence and uniqueness of a global solution. We also study the asymptotic behavior of the solution, and prove that in the case $c$ is sufficiently small, the volume of the tumor cannot expand unlimitedly. It will either disappear or evolve to a dormant state as $t\rightarrow\infty.$

Keywords:  Tumors, Parabolic equations, Global solution, Asymptotic behavior.
Mathematics Subject Classification:  Primary: 35K57, 35Q92; Secondary: 39B12.

Received: December 2009;      Revised: February 2010;      Published: October 2010.

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