On a Class of Reaction-Diffusion Equations with Aggregation

Abstract

In this paper, global-in-time existence and blow-up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis). Properties of the corresponding steady-state problem are also presented. Moreover, the stability around constant equilibria and the non-existence of nonconstant solutions are studied in certain cases.

Keywords

• reaction-diffusion with aggregation
• global existence of classical solutions
• blow-up
• stability
• 35b44
• 35k57
• 35b09
• 35k10