Asymptotic Stability of the Stationary Solution for a Hyperbolic Free Boundary Problem Modeling Tumor Growth
| dc.creator | Cui, Shangbin | |
| dc.date | 2007-12-15 | |
| dc.date.accessioned | 2026-07-07T08:49:31Z | |
| dc.date.available | 2026-07-07T08:49:31Z | |
| dc.description | In this paper we study asymptotic behavior of solutions for a free boundary problem modeling the growth of tumors containing two species of cells: proliferating cells and quiescent cells. This tumor model was proposed by Pettet et al in {\em Bull. Math. Biol.} (2001). By using a functional approach and the $C_0$ semigroup theory, we prove that the unique stationary solution of this model ensured by the work of Cui and Friedman ({\em Trans. Amer. Math. Soc.}, 2003) is locally asymptotically stable in certain function spaces. Key techniques used in the proof include an improvement of the linear estimate obtained by the work of Chen et al ({\em Trans. Amer. Math. Soc.}, 2005), and a similarity transformation. | |
| dc.identifier | https://arxiv.org/abs/0712.2484 | |
| dc.identifier | http://arxiv.org/abs/0712.2484 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144323 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 34G20, 35C10, 92C15. | |
| dc.title | Asymptotic Stability of the Stationary Solution for a Hyperbolic Free Boundary Problem Modeling Tumor Growth | |
| dc.type | text |