Self-similarity in chemotaxis systems
We consider a system which describes the scaling limit of several chemotaxis systems. We focus on self-similarity, and review some recent results on forward and backward self-similar solutions to the system.
Stability analysis of a model of atherogenesis: an energy estimate approach.
Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems
This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.