Regularity properties of singular degenerate abstract differential equations and applications

TL;DR

This paper investigates the regularity and solvability of singular degenerate differential equations, providing new results on boundary value problems and Cauchy problems with applications in fluid mechanics and environmental engineering.

Contribution

It introduces novel regularity results and solution properties for singular degenerate differential equations, expanding understanding of their applications.

Findings

Uniform separability of boundary value problems established

Optimal regularity properties of Cauchy problems derived

Applications demonstrated in fluid mechanics and pollutant dispersion

Abstract

Singular degenerate differential operator equations are studied. The uniform separability of boundary value problems for degenerate elliptic equation and optimal regularity properties of Cauchy problem for degenerate parabolic equation are obtained. These problems have a numeros applications which occur in fluid mechanics, environmental engineering and atmospheric dispersion of pollutants.