Abstract

The main purpose of this paper is to investigate decay estimates for solutions to the Cauchy problem as well as the estimates for solutions to the corresponding Cauchy-Dirichlet problem in an exterior domain . Here a is a positive constant. The coefficient is supposed to be continuous and positive on the closure . The parameter brings to the model the so-called Levi-stable behavior for the corresponding diffusion stochastic process. Finally, we show the global (in time) existence of energy solutions from evolution spaces to the semilinear models in domain with arbitrarily small initial data.