Kenneth H. Karlsen, Suleyman Ulusoy
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.
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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 http://folk.uio.no/kennethk |
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Süleyman Ulusoy Department of Mathematics Faculty of Education, Zirve University Sahinbey, Gaziantep, 27270, Turkey email: suleyman.ulusoy@zirve.edu.tr http://person.zirve.edu.tr/ulusoy/ |
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