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dc.contributor.authorKemppainen, Jukka
dc.contributor.authorSiljander, Juhana
dc.contributor.authorVergara, Vicente
dc.contributor.authorZacher, Rico
dc.date.accessioned2016-10-26T11:14:50Z
dc.date.available2017-01-05T22:45:10Z
dc.date.issued2016
dc.identifier.citationKemppainen, J., Siljander, J., Vergara, V., & Zacher, R. (2016). Decay estimates for time-fractional and other non-local in time subdiffusion equations in R^d. <i>Mathematische Annalen</i>, <i>366</i>(3), 941-979. <a href="https://doi.org/10.1007/s00208-015-1356-z" target="_blank">https://doi.org/10.1007/s00208-015-1356-z</a>
dc.identifier.otherCONVID_25458365
dc.identifier.otherTUTKAID_68697
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/51686
dc.description.abstractWe prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in R d . An important special case is the timefractional diffusion equation, which has seen much interest during the last years, mostly due to its applications in the modeling of anomalous diffusion processes. We follow three different approaches and techniques to study this particular case: (A) estimates based on the fundamental solution and Young’s inequality, (B) Fourier multiplier methods, and (C) the energy method. It turns out that the decay behaviour is markedly different from the heat equation case, in particular there occurs a critical dimension phenomenon. The general subdiffusion case is treated by method (B) and relies on a careful estimation of the underlying relaxation function. Several examples of kernels, including the ultraslow diffusion case, illustrate our results.
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesMathematische Annalen
dc.subject.othertemporal decay estimates
dc.subject.othertime-fractional diffusion
dc.subject.otherultraslow diffusion
dc.subject.othersubdiffusion
dc.subject.otherfundamental solution
dc.subject.othersubordination
dc.subject.otherFourier multiplier
dc.subject.otherenergy estimates
dc.titleDecay estimates for time-fractional and other non-local in time subdiffusion equations in R^d
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201610244418
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2016-10-24T09:15:03Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange941-979
dc.relation.issn0025-5831
dc.relation.numberinseries3
dc.relation.volume366
dc.type.versionacceptedVersion
dc.rights.copyright© Springer-Verlag Berlin Heidelberg 2016. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.1007/s00208-015-1356-z


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