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- W1805798833 abstract "We consider a family of non-autonomousreaction-diffusion equations $$ u_t=sum_{i,j=1}^N a_{ij}(omegat)partial_ipartial_j u+f(omega t,u)+ g(omega t,x),quad xinmathbb R^Ntag{$text{rm E}_omega$} $$with almost periodic,rapidly oscillating principal part and nonlinear interactions. As$omegato infty$, we prove that the solutions of $(text{rm E}_omega)$converge to the solutions of the averaged equation $$u_t=sum_{i,j=1}^N overline a_{ij}partial_ipartial_j u+overline f(u)+ overline g(x),quad xinmathbb R^N.tag{$text{rm E}_infty$} $$ If $f$ isdissipative, we prove existence and upper-semicontinuity ofattractors for the family $(E_omega)$ as $omegatoinfty$." @default.
- W1805798833 created "2016-06-24" @default.
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- W1805798833 date "2002-12-01" @default.
- W1805798833 modified "2023-10-18" @default.
- W1805798833 title "Attractors and global averaging of non-autonomous reaction-diffusion equations in $mathbb R^N$" @default.
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- W1805798833 doi "https://doi.org/10.12775/tmna.2002.035" @default.
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