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Schauder bases and the decay rate of the heat equation

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Schauder bases and the decay rate of the heat equation

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dc.contributor.author Bonet Solves, José Antonio es_ES
dc.contributor.author Lusky, Wolfgang es_ES
dc.contributor.author Taskinen, Jari es_ES
dc.date.accessioned 2021-01-09T04:32:00Z
dc.date.available 2021-01-09T04:32:00Z
dc.date.issued 2019-09 es_ES
dc.identifier.issn 1424-3199 es_ES
dc.identifier.uri http://hdl.handle.net/10251/158500
dc.description.abstract [EN] We consider the classical Cauchy problem for the linear heat equation and integrable initial data in the Euclidean space R-N. We show that given a weighted L-p-space L-w(p)(R-N) with 1 <= p < infinity and a fast-growing weight w, there are Schauder bases (e(n))(n = 1)(infinity) in L-w(p)(R-N) with the following property: given a positive integer m, there exists n(m) > 0 such that, if the initial data f belong to the closed linear space of e(n) with n >= n(m), then the decay rate of the solution of the heat equation is at least t(-m). Such a basis can be constructed as a perturbation of any given Schauder basis. The proof is based on a construction of a basis of L-w(p)(R-N), which annihilates an infinite sequence of bounded functionals. es_ES
dc.description.sponsorship Open access funding provided by University of Helsinki including Helsinki University Central Hospital. The authors would like to thank Thierry Gallay (Grenoble) for discussions which helped in the final formulation of our results. The research of Bonet was partially supported by the projects MTM2016-76647-P and GV Prometeo 2017/102. The research of Taskinen was partially supported by the research grant from the Faculty of Science of the University of Helsinki. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Journal of Evolution Equations es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Schauder bases and the decay rate of the heat equation es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00028-019-00492-x es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2016-76647-P/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2019). Schauder bases and the decay rate of the heat equation. Journal of Evolution Equations. 19(3):717-728. https://doi.org/10.1007/s00028-019-00492-x es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s00028-019-00492-x es_ES
dc.description.upvformatpinicio 717 es_ES
dc.description.upvformatpfin 728 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 19 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\404831 es_ES
dc.contributor.funder Helsingin Yliopisto es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
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