Name
Abstract | ||
|---|---|---|
This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue (extracellular matrix (ECM)). The model consists of a parabolic chemotaxis-haptotaxis PDE describing the evolution of cancer cell density, a parabolic PDE governing the evolution of matrix degrading enzyme concentration, and an ODE reflecting the degradation of ECM. Following a recent approach proposed by Szymanska, Morales-Rodrigo, Lachowicz, and Chaplain [Math. Models Methods Appl. Sci., 19 (2009), pp. 257-281], we assume that the migration of cancer cells through ECM is more like movement in a porous medium. Accordingly, we consider the self-diffusion coefficient D(u) of cancer cells to be a nonlinear function generalizing the prototype D(u) = (u + 1)(m-1) for some m >= 1. Under the assumption that either n <= 8 and m > (2n(2) + 4n - 4)/(n(2) + 4n), or n >= 9 and m > (2n(2) + 3n + 2 - root 8n(n + 1))/(n(2) + 2n) (where n denotes the space dimension), and in the presence of logistic dampening of cancer cell densities, the global existence of a unique classical solution to the model is proved by developing some L-p-estimate techniques that appear to be new in the context of chemotaxis-haptotaxis systems. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/100802943 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
chemotaxis,haptotaxis,nonlinear diffusion,logistic source,cancer invasion model,global existence | Parabolic partial differential equation,Chemotaxis,Mathematical optimization,Nonlinear system,Matrix (mathematics),Nonlinear diffusion,Haptotaxis,Ode,Mathematics,Parabola | Journal |
Volume | Issue | ISSN |
43 | 2 | 0036-1410 |
Citations | PageRank | References |
11 | 1.89 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Youshan Tao | 1 | 22 | 7.04 |
| Michael Winkler | 2 | 23 | 5.52 |