Nonlocal diffusion, a Mittag-Leffler function and a two-dimensional Volterra integral equation
McKee, S. and Cuminato, J. A. (2015) Nonlocal diffusion, a Mittag-Leffler function and a two-dimensional Volterra integral equation. Journal of Mathematical Analysis and Applications, 423 (1). pp. 243-252. ISSN 0022-247X (https://doi.org/10.1016/j.jmaa.2014.09.067)
Preview |
Text.
Filename: McKee_Cuminato_JMAA_2015_Nonlocal_diffusion_a_Mittag_Leffler_function_and_a_two_dimensional_Volterra.pdf
Final Published Version Download (283kB)| Preview |
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.
-
-
Item type: Article ID code: 67553 Dates: DateEvent1 March 2015Published2 October 2014Published OnlineSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 11 Apr 2019 13:35 Last modified: 22 Sep 2024 01:01 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/67553