Spherically restricted random hyperbolic diffusion

Broadbridge, Philip, Kolesnik, Alexander D., Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, Olenko, Andryi and Omari, Dareen 2020. Spherically restricted random hyperbolic diffusion. Entropy 22 (2) , 217. 10.3390/e22020217

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Abstract

This paper investigates solutions of hyperbolic diffusion equations in R 3 R3 with random initial conditions. The solutions are given as spatial-temporal random fields. Their restrictions to the unit sphere S 2 S2 are studied. All assumptions are formulated in terms of the angular power spectrum or the spectral measure of the random initial conditions. Approximations to the exact solutions are given. Upper bounds for the mean-square convergence rates of the approximation fields are obtained. The smoothness properties of the exact solution and its approximation are also investigated. It is demonstrated that the Hölder-type continuity of the solution depends on the decay of the angular power spectrum. Conditions on the spectral measure of initial conditions that guarantee short- or long-range dependence of the solutions are given. Numerical studies are presented to verify the theoretical findings.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	MDPI
ISSN:	1099-4300
Date of First Compliant Deposit:	5 February 2020
Date of Acceptance:	5 February 2020
Last Modified:	13 Nov 2023 14:14
URI:	https://orca.cardiff.ac.uk/id/eprint/129357

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