Asymptotic behavior of solutions of a free boundary problem modeling multi-layer tumor growth in presence of inhibitor

作者：Hou; Xiu Mei

来源：Acta Mathematica Sinica-English Series, 2011, 27(8): 1621-1636.

DOI：10.1007/s10114-011-8361-2

• Free boundary problem
• multi-layer tumor
• inhibitor
• well-posedness
• asymptotic behavior

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 in little Holder 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 flat solutions under the non-flat 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.

• 出版日期2011-8
• 单位武汉生物工程学院; 中山大学