Convergence to steady state for the solutions of a nonlocal reaction-diffusion equation

Abstract

We consider a nonlocal reaction-diffusion equation with mass conservation, which was originally proposed by Rubinstein and Sternberg as a model for phase separation in a binary mixture. We study the large time behavior of the solution and show that it converges to a stationary solution as t tends to infinity. We also evaluate the rate of convergence. In some special case, we show that the limit solution is constant.