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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Nonlocal diffusion, a Mittag-Leffler function and a two-dimensional Volterra integral equation

Texto completo
Autor(es):
Mckee, S. [1] ; Cuminato, J. A. [2]
Número total de Autores: 2
Afiliação do(s) autor(es):
[1] Univ Strathclyde, Dept Math & Stat, Glasgow, Lanark - Scotland
[2] ICMC USP Sao Carlos, Dept Matemat Aplicada & Estat, Sao Carlos, SP - Brazil
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: Journal of Mathematical Analysis and Applications; v. 423, n. 1, p. 243-252, MAR 1 2015.
Citações Web of Science: 2
Resumo

In this paper we consider a particular class of two-dimensional singular Volterra integral equations. Firstly we show that these integral equations can indeed arise in practice by considering a diffusion problem with an output flux which is nonlocal in time; this problem is shown to admit an analytic solution in the form of an integral. More crucially, the problem can be re-characterized as an integral equation of this particular class. This example then provides motivation for a more general study: an analytic solution is obtained for the case when the kernel and the forcing function are both unity. This analytic solution, in the form of a series solution, is a variant of the Mittag-Leffler function. As a consequence it is an entire function. A Gronwall lemma is obtained. This then permits a general existence and uniqueness theorem to be proved. (C) 2014 Elsevier Inc. All rights reserved. (AU)

Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
Beneficiário:José Alberto Cuminato
Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs