On the justification of the quasistationary approximation of several parabolic moving boundary problems—Part I

Abstract

We consider nonlinear coupled evolution equations evolving according to different timescales and study the behavior of solutions as their ratio becomes singular. We derive an abstract result and use it to justify rigorously the quasistationary approximation of a moving boundary problem modeling the growth of an avascular tumor. Another application is a quasilinear formulation of the Keller–Segel model on a bounded domain in RN.