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Burgers' equation by non-local shot noise data

Part of: Random vibrations Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Donatas Surgailis  and
Wojbor A. Woyczynski
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Abstract

We study the scaling limit of random fields which are solutions of a non-linear partial differential equation, known as the Burgers equation, under stochastic initial conditions. These are assumed to be of a non-local shot noise type and driven by a Cox process. Previous work by Bulinskii and Molchanov (1991), Surgailis and Woyczynski (1993a), and Funaki et al. (1994) concentrated on the case of local shot noise data which permitted use of techniques from the theory of random fields with finite range dependence. Those are not available for the non-local case being considered in this paper.

Burgers' equation is known to describe various physical phenomena such as non-linear and shock waves, distribution of self-gravitating matter in the universe, and other flow satisfying conservation laws (see e.g. Woyczynski (1993)).

Keywords

NON-LINEAR WAVESSCALING LIMIT

MSC classification

Primary: 60H15: Stochastic partial differential equations
Secondary: 70L05: Random vibrations
Type
Part 6 Stochastic Processes
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 351 - 362
Copyright
Copyright © Applied Probability Trust 1994 

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