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

Gaocheng Yue, Chengkui Zhong

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

Abstract


In 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
$(H^1,q_U(\R^N),H^1,q_\phi(\R^N))$-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


Reaction-diffusion equations; uniform attractors; locally uniform spaces

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