85 citations · 200 across the 7 of their papers we have counts for
7 papers
Optimal continuous dependence estimates for fractional degenerate parabolic equations
Nathael Alibaud, Simone Cifani, Espen Jakobsen
We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fraction…
On numerical methods and error estimates for degenerate fractional convection-diffusion equations
Simone Cifani, Espen R. Jakobsen
First we introduce and analyze a convergent numerical method for a large class of nonlinear nonlocal possibly degenerate convection diffusion equations. Secondly we develop a new K…
Continuous dependence estimates for nonlinear fractional convection-diffusion equations
Nathaël Alibaud, Simone Cifani, Espen R. Jakobsen
We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are n…
On the spectral vanishing viscosity method for periodic fractional conservation laws
Simone Cifani, Espen R. Jakobsen
We introduce and analyze a spectral vanishing viscosity approximation of periodic fractional conservation laws. The fractional part of these equations can be a fractional Laplacian…
Entropy Solution Theory for Fractional Degenerate Convection-Diffusion Equations
Simone Cifani, Espen R. Jakobsen
We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equatio…
The discontinuous Galerkin method for fractional degenerate convection-diffusion equations
Simone Cifani, Espen R. Jakobsen, Kenneth H. Karlsen
We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (Lévy) operator. We prove various sta…