Dynamics of non-autonomous reaction-diffusion equations in locally uniform spaces
KeywordsReaction-diffusion equations, uniform attractors, locally uniform spaces
AbstractIn this paper, we first prove the well-posedness for the
non-autonomous reaction-diffusion equations on the entire space $\R^N$ in the
setting of locally uniform spaces with singular initial data. Then
we study the asymptotic behavior of solutions of such equation and
show the existence of
$\mcA_\mcH_L^q_U(\R^N)(g_0)$ with locally uniform external
forces being translation uniform bounded but not translation compact
in $L_b^p(\R;L^q_U(\R^N))$. We also obtain the uniform attracting property
in the stronger topology.
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