Autor(es)

Mckee, S. ^[1] ; Cuminato, J. A. ^[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

• 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: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs