DYNAMICS OF NON-AUTONOMOUS REACTION-DIFFUSION EQUATIONS IN LOCALLY UNIFORM SPACES

In this paper, we first prove the well-posedness for the non autonomous reaction-diffusion equations on the entire space RN 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-U(1,q)(R-N), H-phi(1,q)(R-N))-uniform(w.r.t. g is an element of H-LUq(R())N (g0)) attractor A(HLUq)(R-N)(g0) with locally uniform external forces being translation uniform bounded but not translation compact in L-b(p)(R; L-U(q)(R-N)). We also obtain the uniform attracting property in the stronger topology.