On adaptation of methods of nonlinear PDEs to fractional diffusion operators

The notions of entropy, kinetic and renormalized solutions yield consistent well-posedness theories for scalar hyperbolic and degenerate parabolic PDEs of convection-diffusion type. In this talk the adaptation of these methods to the fractional version of such PDEs (with addition of a fractional diffusion operator) will be discussed. The talk is based upon joint works of the speaker with N. Alibaud (Besancon, France), M. Bendahmane (Bordeaux, France), A. Ouedraogo (Bobo-Dioulasso, Burkina-Faso).