Spherically Restricted Random Hyperbolic Diffusion

被引：13

作者：

Broadbridge, Philip ^{[1
]}

Kolesnik, Alexander D. ^{[2
]}

Leonenko, Nikolai ^{[3
]}

Olenko, Andriy ^{[1
]}

Omari, Dareen ^{[1
]}

机构：

[1] La Trobe Univ, Dept Math & Stat, Melbourne, Vic 3086, Australia

[2] Inst Math & Comp Sci, Acad St 5, Kishinev 2028, Moldova

[3] Cardiff Univ, Sch Math, Senghennydd Rd, Cardiff CF24 4AG, Wales

来源：

ENTROPY | 2020年 / 22卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

stochastic partial differential equations; hyperbolic diffusion equation; spherical random field; Holder continuity; long-range dependence; approximation errors; cosmic microwave background; RANDOM-FIELDS; PROPAGATION; REGULARITY; LEQUATION;

D O I：

10.3390/e22020217

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper investigates solutions of hyperbolic diffusion equations in R3 with random initial conditions. The solutions are given as spatial-temporal random fields. Their restrictions to the unit sphere 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 Holder-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.

引用

页数：31

共 37 条

[21] Bessel functions: Monotonicity and bounds [J].