Stability of Entropy Solutions for Levy Mixed Hyperbolic-Parabolic Equations

TL;DR

This paper investigates the stability and uniqueness of entropy solutions for Levy mixed hyperbolic-parabolic equations with non-local diffusion, establishing key properties like L1 contraction and continuous dependence.

Contribution

It provides the first rigorous proof of uniqueness and stability for entropy solutions in Levy mixed hyperbolic-parabolic equations with fractional diffusion.

Findings

Proved L1 contraction property for entropy solutions.

Established continuous dependence on initial data.

Demonstrated stability of solutions under Levy process influences.

Abstract

We analyze entropy solutions for a class of Levy mixed hyperbolicparabolic equations containing a non-local (or fractional) diffusion operator originating from a pure jump Levy process. For these solutions we establish uniqueness (L1 contraction property) and continuous dependence results.