## Continuous dependence estimates for fractal/fractional degenerate parabolic equations

Type:
Site:
Date:
29/05/2012 - 14:30 - 15:30
Salle:
P1 010
Orateur:
Nathaël Alibaud
Localisation:
Université de Besançon
Localisation:
France
Document(s):
Résumé:

This talk will be concerned with the equation
$$u_t + \mathrm{div} f (u) + (-\Delta)^{\alpha/2}\varphi(u) = 0,$$
where $\alpha\in(0, 2)$ and $\varphi$ is a nondecreasing nonlinearity. It will focus on continuous dependence estimates with respect to the nonlinearities and the fractional power $\alpha$. The results are optimal and robust as the fractional Laplacian approaches the classical one, thus giving a new proof of the know estimates for classical degenerate parabolic problems.
Joint work with Simone Cifani and Espen R. Jakobsen (Norwegian University of Science and Technology, Trondheim, Norway).