Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774233 | Journal of Differential Equations | 2017 | 24 Pages |
Abstract
This paper deals with the cancer invasion model{ut=ÎuâÏââ
(uâv)âξââ
(uâw)+μu(1âuâw),xâΩ,t>0,vt=Îvâv+u,xâΩ,t>0,wt=âvw+ηw(1âwâu),xâΩ,t>0 in a bounded smooth domain ΩâR2 with zero-flux boundary conditions, where Ï,ξ, μ and η are positive parameters. Compared to previous mathematical studies, the novelty here lies in: first, our treatment of the full parabolic chemotaxis-haptotaxis system; and second, allowing for positive values of η, reflecting processes with self-remodeling of the extracellular matrix. Under appropriate regularity assumptions on the initial data (u0,v0,w0), by using adapted Lp-estimate techniques, we prove the global existence and uniqueness of classical solutions when μ is sufficiently large, i.e., in the high cell proliferation rate regime.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Peter Y.H. Pang, Yifu Wang,