Asymptotic behaviour of solutions to fractional diffusion-convection equations

Abstract

We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective part of the equation. The proof is based on suitable a-priori estimates, among which proving an Oleinik type inequality plays a key role.

24p, typos corrected

References in corpus (5)

• From the long jump random walk to the fractional Laplacian
• Entropy Solution Theory for Fractional Degenerate Convection-Diffusion Equations
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• On convergence of solutions of fractal Burgers equation toward rarefaction waves
• Non-uniqueness of weak solutions for the fractal Burgers equation

Cited by in corpus (4)

• Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection
• Asymptotic behavior of scalar convection-diffusion equations
• Convection-Diffusion Equations with Random Initial Conditions
• Nonlocal degenerate parabolic hyperbolic equations on bounded domains