On Neumann boundary problem for strongly degenerate parabolic-hyperbolic equations on a bounded rectangle

TL;DR

This paper investigates a Neumann boundary problem for strongly degenerate parabolic-hyperbolic equations, establishing the uniqueness and discussing the existence of entropy solutions under specific conditions.

Contribution

It introduces a new notion of entropy solution for the problem and proves its uniqueness, advancing understanding of degenerate equations with Neumann boundary conditions.

Findings

Proved uniqueness of entropy solutions.

Discussed existence conditions for solutions.

Established a framework for analyzing degenerate parabolic-hyperbolic equations.

Abstract

We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness. The existence of entropy solutions is also discussed.