Stability of constant steady states and existence of unbounded solutions in time to a reaction-diffusion equation modelling chemotaxis

摘要

We consider the initial boundary value problem to a reaction-diffusion equation modelling chemotaxis in one space-dimension under Neumann boundary conditions. We study the stability of constant steady states and show that there exists an unbounded solution in time induced by the instability of constant steady states. (C) 2004 Elsevier Ltd. All rights reserved.