Some qualitative properties for the total variation flow

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• dc.contributor.author Andreu, Fuensanta
• dc.contributor.author Caselles, Vicente
• dc.contributor.author Díaz, Jesus Ildefonso
• dc.contributor.author Mazón, José
• dc.date.accessioned 2018-12-19T13:51:44Z
• dc.date.available 2018-12-19T13:51:44Z
• dc.date.issued 2002
• dc.description.abstract We prove the existence of a finite extinction time for the solutions of the Dirichlet problem for the total variation flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptotic profile of the solutions of the Dirichlet problem is also studied. It is shown that the profiles are nonzero solutions of an eigenvalue-type problem that seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p-Laplacian operator. Finally, the study of the radially symmetric case allows us to point out other qualitative properties that are peculiar of this special class of quasilinear equations.en
• dc.description.sponsorship The first and fourth authors have been partially support by the Spanish DGICYT, Project PB98-1442, the third author by the REN2000-0766. The second author acknowledges partial support by the TMR European Project ‘‘Viscosity Solutions and their Applications’’, Reference FMRXCT98-0234 and the PNPGC Project BFM2000-0962-C02-01.
• dc.format.mimetype application/pdf
• dc.identifier.citation Andreu F, Caselles V, Díaz JI, Mazón JM. Some qualitative properties for the total variation flow. J Funct Anal. 2002 Feb 1;188(2):516-47. DOI: 10.1006/jfan.2001.3829
• dc.identifier.doi http://dx.doi.org/10.1006/jfan.2001.3829
• dc.identifier.issn 0022-1236
• dc.identifier.uri http://hdl.handle.net/10230/36151
• dc.language.iso eng
• dc.publisher Elsevier
• dc.relation.ispartof Journal of Functional Analysis. 2002 Feb 1;188(2):516-47.
• dc.rights © Elsevier http://dx.doi.org/10.1006/jfan.2001.3829
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Total variation flow
• dc.subject.keyword Nonlinear parabolic equations
• dc.subject.keyword Asymptotic behaviour
• dc.subject.keyword Eigenvalue type problem
• dc.subject.keyword Propagation of the support
• dc.title Some qualitative properties for the total variation flow
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion