| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Strathclyde, Dept Math & Stat, Glasgow, Lanark - Scotland
[2] ICMC USP Sao Carlos, Dept Matemat Aplicada & Estat, Sao Carlos, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 423, n. 1, p. 243-252, MAR 1 2015. |
| Web of Science Citations: | 2 |
| Abstract | |
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) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |