TY - JOUR
AU - Yue, Gaocheng
AU - Zhong, Chengkui
PY - 2015/12/01
Y2 - 2022/01/22
TI - Dynamics of non-autonomous reaction-diffusion equations in locally uniform spaces
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 46
IS - 2
SE -
DO - 10.12775/TMNA.2015.073
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2015.073
SP - 935 - 966
AB - In this paper, we first prove the well-posedness for the<br />non-autonomous reaction-diffusion equations on the entire space $\R^N$ in the<br />setting of locally uniform spaces with singular initial data. Then<br />we study the asymptotic behavior of solutions of such equation and<br />show the existence of<br />$(H^1,q_U(\R^N),H^1,q_\phi(\R^N))$-uniform(w.r.t.<br />$g\in\mcH_L^q_U(\R^N)(g_0)$) attractor<br />$\mcA_\mcH_L^q_U(\R^N)(g_0)$ with locally uniform external<br />forces being translation uniform bounded but not translation compact<br />in $L_b^p(\R;L^q_U(\R^N))$. We also obtain the uniform attracting property<br />in the stronger topology.
ER -