Nonlinear abstract boundary value problems modelling atmospheric dispersion of pollutants

The boundary value problems for linear and nonlinear degenerate elliptic differential-operator equations of a second order are studied. The principal parts of these problems possess variable coefficients and corresponding differential operators are non-self-adjoint. Several conditions for the separability, RR-positivity and the fredholmness in abstract LpLp-spaces are given. By using these results the existence, uniqueness and the maximal regularity of boundary value problems for nonlinear degenerate parabolic differential-operator equations are established. In applications mixed boundary value problems for degenerate diffusion systems, appearing in the atmospheric dispersion of pollutants are studied.