Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of multi-layer tumors
Fujun Zhou, Junde Wu, Shangbin Cui · Communications on Pure & Applied Analysis · 2009
In this paper we study a moving boundary problem modeling the growth of multi-layer tumors under the action of inhibitors. The problem contains two coupled reaction-diffusion equations and one elliptic equation defined on a strip-like domain in $R^n$, with one part of the boundary moving and a priori unknown. The evolution of the moving boundary is governed by a Stefan type equation, with the surface tension effect taken into consideration. Local existence and asymptotic behavior of solutions to this problem are investigated. The analysis is based on the employment of the functional analysis method combing with the well-posedness and geometric theory for parabolic differential equations in Banach spaces.