Juan Luis Vázquez Suárez: Nonlinear Diffusion with Fractional Operators

Coffee: 15:30 - 16:00
 

Abstract: I will report on some of the progress made with collaborators on the topic of nonlinear diffusion equations involving long distance interactions, mostly in the form of fractional Laplacian operators. The nonlinearities are of the following types: porous medium, fast diffusion or p-Laplacian. Differences with standard diffusion have been specially examined. Results cover well-posedness, regularity, free boundaries, asymptotics and entropies, ultracontractive bounds, and others.