Communications in Mathematical Sciences
Volume 15 (2017)
Global weak solutions to a strongly degenerate haptotaxis model
Pages: 1581 – 1616
We consider a one-dimensional version of a model obtained in [C. Engwer, A. Hunt, and C. Surulescu, IMA J. Math. Med. Biol., 33(4):435–459, 2016] and describing the anisotropic spread of tumor cells in a tissue network. The model consists of a reaction-diffusion-taxis equation for the density of tumor cells coupled with an ODE for the density of tissue fibers and allows for strong degeneracy both in the diffusion and the haptotaxis terms. In this setting we prove the global existence of weak solutions to an associated no-flux initial-boundary value problem. Numerical simulations are performed in order to illustrate the model behavior.
haptotaxis, degenerate diffusion, global existence
2010 Mathematics Subject Classification
Primary 35K51, 35K57, 35K65. Secondary 35D30, 35K55, 35Q30, 35Q92, 92C17.
Paper received on 23 June 2016.