Attractors and global averaging of non-autonomous reaction-diffusion equations in $\mathbb R^N$
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Evolution process, attractor, almost periodic function, averagingAbstrakt
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 $\omega\to\infty$.Pobrania
Opublikowane
2002-12-01
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1.
ANTOCI, Francesca & PRIZZI, Martino. Attractors and global averaging of non-autonomous reaction-diffusion equations in $\mathbb R^N$. Topological Methods in Nonlinear Analysis [online]. 1 grudzień 2002, T. 20, nr 2, s. 229–259. [udostępniono 22.7.2024].
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