Attractors for reaction-diffusion equations on arbitrary unbounded domains

Martino Prizzi, Krzysztof P. Rybakowski

DOI: http://dx.doi.org/10.12775/TMNA.2007.029

Abstract


We prove existence of global attractors for parabolic
equations of the form
$$
\alignedat2
u_t+\beta(x)u-
\sum_{ij}\partial_i(a_{ij}(x)\partial_j u)&=f(x,u),&\quad &x\in
\Omega,\ t\in[0,\infty[,\\
u(x,t)&=0,&\quad &x\in \partial \Omega,\ t\in[0,\infty[.
\endalignedat
$$
on an arbitrary unbounded domain $\Omega$ in $\mathbb R^3$, without
smoothness assumptions on $a_{ij}(\cdot)$ and $\partial\Omega$.

Keywords


Attractors; reaction-diffusion equations; fractional power spaces; tail-estimates

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