Cauchy problem with subcritical nonlinearity

[摘要] The semilinear parabolic system on R-n with subcritical nonlinearity is studied as an abstract evolutionary equation in a Banach space X = L-p(R-n). As in the case of bounded domains the existence of a strongly continuous semigroup of global X-alpha-solutions and its dissipativeness is shown to follow from a single estimate of solutions. Despite the lack of compactness of the Sobolev embeddings in R-n the compactness of trajectories of the semigroup is proved using the auxiliary estimate of solutions in a weighted space L-p(R-n,(1 + \x\(2))(nu)), and the existence of a global attractor is also shown. Thus this paper generalizes earlier considerations and provides a basis for further applications. (C) 1997 Academic Press.

[发布日期] 1997-06-15