Uniform boundedness in a n-dimensional tumor invasion system with chemotaxis effect

Sachiko Ishida
Chiba University

We consider the initial-boundary value problem for a degenerate chemotaxis model arising from tumor invasion which was proposed Fujie-Ito-Yokota (2014). This model describes that tumor cells reduce its surrounding tissue and migrate toward blood vessels. Since it has chemotactic property, it is expected that the behavior of a solution (blow-up, bounded) will depend on parameters of diffusion coefficient and aggregation coefficient. In this talk, we will start with the classic Keller-Segel system and then will discuss uniform boundedness of solution for the tumor model via maxial Sobolev regularity.