Asymptotic Behavior of Solutions of a Free Boundary Problem Modeling Multi-layer Tumor Growth in Presence of Inhibitor  

作　　者：Xiu Mei HOU 

机构地区：[1]Wuhan Bioengineering Institute, Wuhan 430415, P. R. China [2]Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第8期1621-1636,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 10771223）

摘　　要：In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed i[n little H61der spaces. Next we investigate asymptotic behavior of the solution. By computing the spectrum of the linearized problem and using the linearized stability theorem, we give the rigorous analysis of stability and instability of all stationary fiat solutions under the non-fiat perturbations. The method used in proving these results is first to reduce the free boundary problem to a differential equation in a Banach space, and next use the abstract well-posedness and geometric theory for parabolic differential equations in Banach spaces to make the analysis.In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed i[n little H61der spaces. Next we investigate asymptotic behavior of the solution. By computing the spectrum of the linearized problem and using the linearized stability theorem, we give the rigorous analysis of stability and instability of all stationary fiat solutions under the non-fiat perturbations. The method used in proving these results is first to reduce the free boundary problem to a differential equation in a Banach space, and next use the abstract well-posedness and geometric theory for parabolic differential equations in Banach spaces to make the analysis.

关 键 词：Free boundary problem multi-layer tumor INHIBITOR WELL-POSEDNESS asymptotic behavior 

分 类 号：O175.2[理学—数学] Q26[理学—基础数学]