ASYMPTOTIC STABILITY OF THE STATIONARY SOLUTION FOR A PARABOLIC-HYPERBOLIC FREE BOUNDARY PROBLEM MODELING TUMOR GROWTH?

摘要

This paper studies asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with two species of cells: proliferating cells and quiescent cells. In previous literature it has been proved that this problem has a unique stationary solution which is asymptotically stable in the limit case ε = 0. In this paper we consider the more realistic case 0 < ε 1. In this case, after suitable reduction the model takes the form of a coupled system of a parabolic equation and a hyperbolic system, so that it is more difficult than the limit case ε = 0. By using some unknown variable transform as well as the similarity transform technique developed in our previous work, we prove that the stationary solution is also asymptotically stable in the case 0 < ε 1.