Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 116, pp. 1-23.

Title: Stability of entropy solutions for Levy mixed 
       hyperbolic-parabolic equations

Authors: Kenneth H. Karlsen (Univ. of Oslo, Norway)
         Suleyman Ulusoy (Zirve Univ. Sahinbey, Gaziantep, 27270, Turkey)

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.

Submitted April 25, 2011. Published September 12, 2011.
Math Subject Classifications: 45K05, 35K65, 35L65; 35B65.
Key Words: Degenerate parabolic equation; conservation law; stability;
           fractional Laplacian;  non-local diffusion; entropy solution; 
           uniqueness;  continuous dependence.