Convergence to steady state for the solutions of a nonlocal reaction-diffusion equation
Samira Boussaïd, Danielle Hilhorst, Thanh Nam Nguyen · Evolution equations and control theory · 2015
We consider a nonlocal reaction-diffusion equation with mass conservation, whichwas originally proposed by Rubinstein and Sternberg as a model for phaseseparation 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.