Show simple item record

dc.contributor.authorStan, D.
dc.contributor.authorDel Teso, F.
dc.contributor.authorVázquez, J.L.
dc.date.accessioned2017-10-06T09:15:12Z
dc.date.available2017-10-06T09:15:12Z
dc.date.issued2017-10
dc.identifier.issn0003-9527
dc.identifier.urihttp://hdl.handle.net/20.500.11824/739
dc.description.abstractWe 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 $0<s<1$, we assume that the solutions are non-negative and the problem is posed in the whole space. In this paper we prove existence of weak solutions for all integrable initial data $u_0 \ge 0$ and for all exponents $m>1$ 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.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectNonlinear fractional diffusionen_US
dc.subjectfractional Laplacianen_US
dc.subjectexistence of weak solutionsen_US
dc.subjectenergy estimatesen_US
dc.subjectspeed of propagationen_US
dc.subjectsmoothing effecten_US
dc.subjectnumerical simulationsen_US
dc.titleExistence of weak solutions for a general porous medium equation with nonlocal pressureen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.arxiv1609.05139
dc.relation.publisherversionhttps://arxiv.org/abs/1609.05139en_US
dc.relation.projectIDES/1PE/SEV-2017-0718en_US
dc.relation.projectIDEUS/BERC/BERC.2018-2021en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/submittedVersionen_US
dc.journal.titlesubmitteden_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España