### Dynamics of non-autonomous reaction-diffusion equations in locally uniform spaces

DOI: http://dx.doi.org/10.12775/TMNA.2015.073

#### Abstract

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

$(H^1,q_U(\R^N),H^1,q_\phi(\R^N))$-uniform(w.r.t.

$g\in\mcH_L^q_U(\R^N)(g_0)$) attractor

$\mcA_\mcH_L^q_U(\R^N)(g_0)$ 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.

#### Keywords

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