Stochastic Degenerate Fractional Conservation Laws

TL;DR

This paper studies stochastic degenerate fractional conservation laws, establishing existence, uniqueness, and continuous dependence of solutions on various parameters using an adapted kinetic formulation.

Contribution

It introduces a unified framework for analyzing stochastic degenerate fractional conservation laws with continuous dependence estimates.

Findings

Proved existence and uniqueness of solutions.

Established L^1-continuous dependence on initial data and parameters.

Developed a kinetic formulation approach for these laws.

Abstract

We consider the Cauchy problem for a degenerate fractional conservation laws driven by a noise. In particular, making use of an adapted kinetic formulation, a result of existence and uniqueness of solution is established. Moreover, a unified framework is also established to develop the continuous dependence theory. More precisely, we demonstrate L^1-continuous dependence estimates on the initial data, the order of fractional Laplacian, the diffusion matrix, the flux function, and the multiplicative noise function present in the equation.