On the structure of entropy solutions to the Riemann problem for a degenerate nonlinear parabolic equation

TL;DR

This paper derives explicit entropy solutions for a Riemann problem involving a degenerate nonlinear parabolic equation with piecewise coefficients, showing these solutions minimize a convex function.

Contribution

It provides an explicit form of entropy solutions for a specific degenerate nonlinear parabolic equation, linking solutions to convex optimization.

Findings

Explicit entropy solutions are obtained for the Riemann problem.

Solutions correspond to the minimum of a convex function.

The approach clarifies the structure of solutions for degenerate equations.

Abstract

We find an explicit form of entropy solutions to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is demonstrated that this solution corresponds to the minimum point of some strictly convex function of a finite number of variables.