Stochastic Degenerate Fractional Conservation Laws
Analysis of PDEs
2021-09-27 v1
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.
Keywords
Cite
@article{arxiv.2109.11889,
title = {Stochastic Degenerate Fractional Conservation Laws},
author = {Abhishek Chaudhary},
journal= {arXiv preprint arXiv:2109.11889},
year = {2021}
}
Comments
33 pages. arXiv admin note: text overlap with arXiv:1309.5817, arXiv:1202.2031 by other authors