Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity. (October 2016) - Xie, Yongqin; Li, Qingsong; Zhu, Kaixuan
Abstract: In this paper, using a new method (or technique) called "Asymptotic Contractive Semigroup Method" (seeTheorem 2.3 ) we prove the existence of global attractor for the nonclassical diffusion equations in H 1 ( R n ) . The nonlinearity satisfies the arbitrary order polynomial growth conditions and the forcing term g only belongs to H − 1 ( R n ) . The results obtained essentially improve and complement in some previously published papers.