Weak Asymptotic Methods For Scalar Equations And Systems

dc.creatorAbreu
dc.creatorEduardo; Colombeau
dc.creatorMathilde; Panov
dc.creatorEugeny
dc.date2016
dc.datedez
dc.date2017-11-13T11:32:41Z
dc.date2017-11-13T11:32:41Z
dc.date.accessioned2018-03-29T05:47:16Z
dc.date.available2018-03-29T05:47:16Z
dc.identifierJournal Of Mathematical Analysis And Applications. Academic Press Inc Elsevier Science, v. 444, p. 1203 - 1232, 2016.
dc.identifier0022-247X
dc.identifier1096-0813
dc.identifierWOS:000381956400020
dc.identifier10.1016/j.jmaa.2016.06.047
dc.identifierhttp://www-sciencedirect-com.ez88.periodicos.capes.gov.br/science/article/pii/S0022247X16302840
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/326120
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1363126
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionIn this paper we show how one can construct families of continuous functions which satisfy asymptotically scalar equations with discontinuous nonlinearity and systems having irregular solutions. This construction produces weak asymptotic methods which are issued from Maslow asymptotic analysis. We obtain a sequence of functions which tend to satisfy the equation(s) in the weak sense in the space variable and in the strong sense in the time variable. To this end we reduce the partial differential equations to a family of ordinary differential equations in a classical Banach space. For scalar equations we prove that the initial value problem is well posed in the L-1 sense for the approximate solutions we construct. Then we prove that this method gives back the widely accepted solutions when they are known. For systems we obtain existence in the general case and uniqueness in the analytic case using an abstract Cauchy-Kovalevska theorem. (C) 2016 Published by Elsevier Inc.
dc.description444
dc.description2
dc.description1203
dc.description1232
dc.descriptionFAPESP [2014/103204-9, 2012/15780-9]
dc.descriptionCNPq [445758/2014-7]
dc.descriptionRFBR [15-01-07650-a]
dc.descriptionMES of Russia [1.445.2016/PhiIIM]
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.languageEnglish
dc.publisherAcademic Press Inc Elsevier Science
dc.publisherSan Diego
dc.relationJournal of Mathematical Analysis and Applications
dc.rightsfechado
dc.sourceWOS
dc.subjectPartial Differential Equations
dc.subjectFunctional Analysis
dc.subjectMaslov Asymptotic Analysis
dc.subjectInitial Value Problem
dc.subjectOrdinary Differential Equations
dc.titleWeak Asymptotic Methods For Scalar Equations And Systems
dc.typeArtículos de revistas


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