Traveling Waves for a Tumor Growth System

We consider a model of tumor growth suggested by [Luckhaus-Triolo], which emphasizes the competition for space rather than for nutrients. In their work a coupled system of a parabolic and an ordinary differential equation is derived describing the density evolution of mutant and the nearly stationary healthy cells. Especially, the question is raised if healthy tissue is able to prevent mutant cells to invade. In our project we consider the asymptotic propagation of initially separated cell populations. Here we present the traveling wave problem for the model described above and show existence of waves by a vanishing viscosity approach. In particular, a unique monotone wave exists, which, depending on an associated Lyapunov functional, either invades the healthy tissue or is stationary and discontinuous. However, the discontinuous wave is not stable.

This is an ongoing joint work with Steffen Heinze and Ben Schweizer.