dc.contributor.author Stan, D. dc.contributor.author Del Teso, F. dc.contributor.author Vázquez, J.L. dc.date.accessioned 2017-10-06T09:15:12Z dc.date.available 2017-10-06T09:15:12Z dc.date.issued 2017-10 dc.identifier.issn 0003-9527 dc.identifier.uri http://hdl.handle.net/20.500.11824/739 dc.description.abstract We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters $m>1$ and $01$ by developing a new approximating method that allows to treat the range $m\ge 3$ that could not be covered by previous works. We also consider as initial data any non-negative measure $\mu$ with finite mass. In passing from bounded initial data to measure data we make strong use of an $L^1$-$L^\infty$ smoothing effect and other functional inequalities. Finite speed of propagation is established for all $m\ge 2$, which implies the existence of free boundaries. The authors had already proved that finite propagation does not hold for $m<2$. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Nonlinear fractional diffusion en_US dc.subject fractional Laplacian en_US dc.subject existence of weak solutions en_US dc.subject energy estimates en_US dc.subject speed of propagation en_US dc.subject smoothing effect en_US dc.subject numerical simulations en_US dc.title Existence of weak solutions for a general porous medium equation with nonlocal pressure en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.arxiv 1609.05139 dc.relation.publisherversion https://arxiv.org/abs/1609.05139 en_US dc.relation.projectID ES/1PE/SEV-2017-0718 en_US dc.relation.projectID EUS/BERC/BERC.2018-2021 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/submittedVersion en_US dc.journal.title submitted en_US
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