Nonlinear diffusion with fractional Laplacian operators

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• Juan Luis Vázquez (Universidad Autónoma de Madrid)
• Wednesday 09 April 2014, 16:00-17:00
• Room R17/18, Watson building.

If you have a question about this talk, please contact José Cañizo.

Joint Applied Math-Analysis seminar

Much recent research is taking place in the area of elliptic and parabolic equations, aimed at understanding the effect of replacing the Laplace operator, and its usual variants, by a fractional Laplacian operator or other similar nonlocal operators, which represent long distance interactions. Linear and nonlinear models are involved.

The lecture will describe some of the progress made by the author and collaborators on the topic of nonlinear fractional heat equations, in particular when the nonlinearities are of porous medium and fast diffusion type. The results cover existence and uniqueness of weak (sometimes classical) solutions, regularity and continuous dependence, positivity, estimates and symmetrization. Attention is given to the construction of fractional Barenblatt solutions and their asymptotic role.

This talk is part of the Analysis Seminar series.

This talk is included in these lists:

• Analysis Seminar
• Room R17/18, Watson building
• School of Mathematics Events

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