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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 epsilon = 0. In this paper we consider the more realistic case 0 < epsilon << 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 epsilon = 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 < epsilon << 1.
- 出版日期2013
- 单位中山大学
