Stefano Lisini (Pavia)
An existence result for fractional porous medium equations
In this talk I will show a construction of weak global solutions for
a family of fractional porous medium equation. A proof based on the gradient flow interpretation extends to a very general class of initial data the previous results of Caffarelli-Vazquez.
An energy dissipation inequality and the monotonicity of the L^p norms along the solutions will be illustrated.
Finally I will show the convergence of the solutions of the s-fractional porous medium equation to the unique solution of the classical porous medium equation as the parameter s goes to 0.
This talk is based on joint work with E. Mainini and A. Segatti.