Convergence to steady states for solutions of a reaction-diffusion equation with mass conservation

Samira Boussaïd (1) , Danielle Hilhorst (2) , Thanh Nam Nguyen (2)

1 Université Hadj Lakhdar Batna 1
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We consider a nonlocal reaction-diffusion equation with mass con- servation, 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.

Domaines: Equations aux dérivées partielles [math.AP]

Samira Boussaïd, Danielle Hilhorst, Thanh Nam Nguyen. Convergence to steady states for solutions of a reaction-diffusion equation with mass conservation. 2015. ⟨hal-00817614v2⟩