Nonlocal dissipation measure and L1 kinetic theory for fractional conservation laws
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In this article, a kinetic formulation for scalar conservation laws with nonlocal and nonlinear diffusion terms is introduced, dealing with merely L 1 initial data, general self-adjoint pure jump Levy operators, and general non-local diffusion terms.Abstract:
We introduce a kinetic formulation for scalar conservation laws with nonlocal and nonlinear diffusion terms. We deal with merely L1 initial data, general self-adjoint pure jump Levy operators, and ...read more
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References
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Book
Foundations of Modern Potential Theory
TL;DR: In this paper, the authors define the notion of potentials and their basic properties, including the capacity and capacity of a compact set, the properties of a set of irregular points, and the stability of the Dirichlet problem.
Journal ArticleDOI
A kinetic formulation of multidimensional scalar conservation laws and related equations
Journal ArticleDOI
Entropy Solutions for Nonlinear Degenerate Problems
TL;DR: In this article, the existence of entropy solutions for two classes of elliptic-parabolic-hyperbolic degenerate equations with Dirichlet homogeneous boundary conditions was proved.