Singular Degenerate Differential Operators and Applications

The boundary value problems for linear and nonlinear singular degenerate differential-operator equations with variable coefficients are studied. Degenerate linear problems are considered on the moving domain. The uniform maximal regularity properties of the singular degenerate linear problem with parameters and the existence and uniqueness result for the degenerate nonlinear problem is shown. This problem occur in fluid mechanics and environmental engineering.

DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS OF HIGHER ORDER AND ARBITRARY WEIGHT

We consider the Dirichlet problem for a degenerate differential-operator equation of higher order with arbitrary weight-function ρ(t). We establish some embedding and compactness theorems in weighted Sobolev spaces, show existence and uniqueness of the generalized solutions. We also give a description of the spectrum for the corresponding operator.

Degenerate Differential Operators with Parameters

The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. The principal parts of the appropriate generated differential operators are non-self-adjoint. Several conditions for the maximal regularity uniformly with respect to the parameter and the Fredholmness in Banach-valuedLp−spaces of these problems are given. In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.