An Approach Without Using Hardy Inequality For The Linear Heat Equation With Singular Potential

dc.creatorFerreira
dc.creatorLucas C. F.; Mesquita
dc.creatorClaudia Aline A. S.
dc.date2015-OCT
dc.date2016-06-07T13:19:33Z
dc.date2016-06-07T13:19:33Z
dc.date.accessioned2018-03-29T01:39:44Z
dc.date.available2018-03-29T01:39:44Z
dc.identifier
dc.identifierAn Approach Without Using Hardy Inequality For The Linear Heat Equation With Singular Potential. World Scientific Publ Co Pte Ltd, v. 17, p. OCT-2015.
dc.identifier0219-1997
dc.identifierWOS:000362560100013
dc.identifier10.1142/S0219199715500418
dc.identifierhttp://www.worldscientific.com/doi/10.1142/S0219199715500418
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/242715
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1306413
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionThe aim of this paper is to employ a strategy known from fluid dynamics in order to provide results for the linear heat equation u(t) - Delta u - V (x)u = 0 in R-n with singular potentials. We show well-posedness of solutions, without using Hardy inequality, in a framework based in the Fourier transform, namely, PMk-spaces. For arbitrary data u(0) is an element of PMk, the approach allows to compute an explicit smallness condition on V for global existence in the case of V with finitely many inverse square singularities. As a consequence, well-posedness of solutions is obtained for the case of the monopolar potential V (x) = lambda/vertical bar x vertical bar(2) with vertical bar lambda vertical bar < lambda(*) = (n-2)(2)/4. This threshold value is the same one obtained for the global well-posedness of L-2-solutions by means of Hardy inequalities and energy estimates. Since there is no any inclusion relation between L-2 and PMk, our results indicate that lambda(*) is intrinsic of the PDE and independent of a particular approach. We also analyze the long-time behavior of solutions and show there are infinitely many possible asymptotics characterized by the cells of a disjoint partition of the initial data class PMk.
dc.description17
dc.description5
dc.description
dc.description
dc.description
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description
dc.description
dc.description
dc.languageen
dc.publisherWORLD SCIENTIFIC PUBL CO PTE LTD
dc.publisher
dc.publisherSINGAPORE
dc.relationCOMMUNICATIONS IN CONTEMPORARY MATHEMATICS
dc.rightsfechado
dc.sourceWOS
dc.subjectNavier-stokes Equations
dc.subjectSelf-similar Solutions
dc.subjectParabolic Equations
dc.subjectElliptic-equations
dc.subjectSchrodinger-operators
dc.subjectCritical Growth
dc.subjectExistence
dc.subjectNonexistence
dc.subjectStability
dc.subjectTerm
dc.titleAn Approach Without Using Hardy Inequality For The Linear Heat Equation With Singular Potential
dc.typeArtículos de revistas


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