Stability of Entropy Solutions for Levy Mixed Hyperbolic-Parabolic Equations

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.

20 pages, no figures. Manuscript submitted to Elseiver

References in corpus (4)

• Regularity theory for fully nonlinear integro-differential equations
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• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
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Cited by in corpus (7)

• Entropy Solution Theory for Fractional Degenerate Convection-Diffusion Equations
• Continuous dependence estimates for nonlinear fractional convection-diffusion equations
• The discontinuous Galerkin method for fractal conservation laws
• The discontinuous Galerkin method for fractional degenerate convection-diffusion equations
• Well-posedness of nonlinear transport equation by stochastic perturbation
• Asymptotic properties of entropy solutions to fractal Burgers equation
• $L^1$ contraction for bounded (non-integrable) solutions of degenerate parabolic equations