Degenerate Anisotropic Parabolic Problems Occurring in Atmospheric Dispersion of Pollutants

Abstract

In the present paper the boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued L-p-spaces are given. Sharp estimates for resolvent, of the corresponding differential operators are obtained. By using these results the existence, uniqueness and the maximal regularity of boundary value problems for parabolic differential-operator equations are established. In applications mixed boundary value problems for diffusion systems, appearing in the atmospheric dispersion of pollutants are studied.