Electron. J. Diff. Equ., Vol. 2011 (2011), No. 116, pp. 1-23.

Stability of entropy solutions for Levy mixed hyperbolic-parabolic equations

Kenneth H. Karlsen, Suleyman Ulusoy

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.

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Kenneth Hvistendahl Karlsen
Centre of Mathematics for Applications
University of Oslo
P.O. Box 1053, Blindern, N-0316 Oslo, Norway
email: kennethk@math.uio.no
Süleyman Ulusoy
Department of Mathematics
Faculty of Education, Zirve University
Sahinbey, Gaziantep, 27270, Turkey
email: suleyman.ulusoy@zirve.edu.tr

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