Stability of entropy solutions for Levy mixed hyperbolic-parabolic equations

Abstract

We analyze entropy solutions for a class of Levy mixed hyperbolic-parabolic equations containing a non-local (or fractional) diffusion operator originating from a pure jump Levy process. For these solutions we establish uniqueness (L^1 contraction property) and continuous dependence results.

Keywords

• Degenerate parabolic equation
• conservation law
• stability
• fractional Laplacian
• non-local diffusion
• entropy solution
• uniqueness
• continuous dependence