Trajectory attractors of reaction-diffusion systems with small diffusion

M. I. Vishik ; V. V. Chepyzhov

Sbornik. Mathematics, Tome 200 (2009) no. 4, pp. 471-497

Résumé

We consider a reaction-diffusion system of two equations, where one equation has a small diffusion coefficient $\delta>0$. We construct the trajectory attractor $\mathfrak A^\delta$ of such a system. We also study the limit system for $\delta=0$. In this system one equation is an ordinary differential equation in $t$, but is considered in the domain $\Omega\times\mathbb R_+$, where $\Omega\Subset\mathbb R^n$ and $\mathbb R_+$ is the positive time axis, $t$. We construct the trajectory attractor $\mathfrak A^0$ of the limit system. The main result is a convergence theorem: $\mathfrak A^\delta\to\mathfrak A^0$ as $\delta\to0^+$ in the corresponding topology. Bibliography: 18 titles.

Détail

Keywords: trajectory attractor
Mots-clés : reaction-diffusion equations.