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dc.contributor.authorDel Teso, F.
dc.contributor.authorEndal, J.
dc.contributor.authorJacobsen, E.R.
dc.date.accessioned2016-09-21T17:39:05Z
dc.date.available2016-09-21T17:39:05Z
dc.date.issued2016-09-01
dc.identifier.issn0001-8708
dc.identifier.urihttp://hdl.handle.net/20.500.11824/307
dc.description.abstractWe study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ can be any nonlocal symmetric degenerate elliptic operator including the fractional Laplacian and numerical discretizations of this operator. The function $\varphi:\mathbb{R} \to \mathbb{R}$ is only assumed to be continuous and nondecreasing. The class of equations include nonlocal (generalized) porous medium equations, fast diffusion equations, and Stefan problems. In addition to very general uniqueness and existence results, we obtain stability, $L^1$-contraction, and a priori estimates. We also study local limits, continuous dependence, and properties and convergence of a numerical approximation of our equations.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.subjectuniquenessen_US
dc.subjectdistributional solutionsen_US
dc.subjectnonlinear degenerate diffusionen_US
dc.subjectporous medium equationen_US
dc.subjectStefan problemen_US
dc.subjectfractional Laplacianen_US
dc.subjectnonlocal operatorsen_US
dc.subjectexistenceen_US
dc.subjectstabilityen_US
dc.subjectlocal limitsen_US
dc.subjectcontinuous dependenceen_US
dc.subjectnumerical approximationen_US
dc.subjectconvergenceen_US
dc.titleUniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Typeen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.aim.2016.09.021
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0001870816300706
dc.relation.projectIDES/1PE/SEV-2013-0323en_US
dc.relation.projectIDEUS/BERC/BERC.2014-2017en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleAdvances in Mathematicsen_US


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