Stochastic Degenerate Fractional Conservation 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.

33 pages. arXiv admin note: text overlap with arXiv:1309.5817, arXiv:1202.2031 by other authors