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Free boundaries in fractional filtration equations

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Free Boundary Problems and Related Topics

Co-authors: Arturo de Pablo (U. Carlos III de Madrid), Ana Rodrguez (U. Politcnica de Madrid), Juan Luis Vzquez (U. Autnoma de Madrid)

In this talk we will review some recent results on the Cauchy problem for the fractional filtration equation $partial_t u+(-Delta) arphi(u)$, $ igmain(0,2)$, where the nonlinearity $ arphi$ satisfies some not very restrictive conditions.

Solutions to these problems become instantaneously positive if the initial data are nonnegative. However, a free boundary emerges in certain cases in which there is a distinguished value, as in the fractional Stefan problem, $ arphi(u)=(u-1)_+$, or in the mesa limit, $m oinfty$, for the fractional porous media equation, $ arphi(u)=um$.

This talk is part of the Isaac Newton Institute Seminar Series series.

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