Attractors and global averaging of non-autonomous reaction-diffusion equations in $\mathbb R^N$
Keywords
Evolution process, attractor, almost periodic function, averagingAbstract
We consider a family of non-autonomous reaction-diffusion equations $$ u_t=\sum_{i,j=1}^N a_{ij}(\omega t)\partial_i\partial_j u+f(\omega t,u)+ g(\omega t,x), \quad x\in\mathbb R^N \tag{$\text{\rm E}_\omega$} $$ with almost periodic, rapidly oscillating principal part and nonlinear interactions. As $\omega\to \infty$, we prove that the solutions of $(\text{\rm E}_\omega)$ converge to the solutions of the averaged equation $$ u_t=\sum_{i,j=1}^N \overline a_{ij}\partial_i\partial_j u+\overline f(u)+ \overline g(x), \quad x\in\mathbb R^N. \tag{$\text{\rm E}_\infty$} $$ If $f$ is dissipative, we prove existence and upper-semicontinuity of attractors for the family $(E_\omega)$ as $\omega\to\infty$.Downloads
Published
2002-12-01
How to Cite
1.
ANTOCI, Francesca and PRIZZI, Martino. Attractors and global averaging of non-autonomous reaction-diffusion equations in $\mathbb R^N$. Topological Methods in Nonlinear Analysis. Online. 1 December 2002. Vol. 20, no. 2, pp. 229 - 259. [Accessed 19 April 2024].
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