Dynamics For A Semilinear Reaction-diffusion Equation With Distribution Derivatives In R~N

In this paper, we prove some asymptotic regularity for a nonlinear reaction-diffusion equation defined on RN(N> 3) with a polynomially growing nonlinearity of arbitrary order and with distribution derivatives in the inhomogeneous term:We get some asymptotic regularity by applying the ideal and result in [39,40, 33]. On the one hand, we prove that the solution u(x, t) go into a more smooth space. On the other hand, we can obtain further characterization of the structure of solutions. We get such a result about the structure of solution: where, v(x) is the the solution of Eq.(3.1.6), and Bδ(?) H1(RN)∩Lp+δ(RN) is more smooth than the solution space.As the application of these asymptotic results, We can obtain the existence of a (L2(RN), L2(RN)∩LP(RN))- global attractor immediately. moreover, such a at-tractor can attract every L2(RN)-bounded set with the L2(RN)∩Lp+δ(RN)-norm for anyδ∈[0,∞). Finally, we get the existence of a(L2(RN),H1(RN))-global attractor.