Singular degenerate problems and applications

TL;DR

This paper investigates boundary value problems for singular degenerate differential-operator equations, establishing well-posedness and regularity results with applications in fluid mechanics, environmental engineering, and atmospheric pollution dispersion.

Contribution

It provides new theoretical results on the well-posedness and regularity of singular degenerate boundary value problems, extending their applicability in various scientific fields.

Findings

Proved well-posedness of linear singular degenerate problems.

Established optimal regularity for nonlinear problems.

Applied results to fluid mechanics and environmental engineering scenarios.

Abstract

The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied. We prove a well-posedeness of linear problem and optimal regularity result for the nonlinear problem which occur in fluid mechanics, environmental engineering and in the atmospheric dispersion of pollutants.