On a stochastic hyperbolic system in linear elasticity

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TR Number
Date
2000-08
Journal Title
Journal ISSN
Volume Title
Publisher
Siam Publications
Abstract

In this paper we discuss the Cauchy problem for linear elasticity with a space-time white noise forcing term. We show that the solution can be represented by a formula analogous to the Riesz formula for solutions of a wave equation. The solution is a generalized stochastic process and is obtained as the limit of a sequence of ordinary stochastic processes. Our basic tool is the Hilbert space method combined with geometric properties of solutions inherent with a hyperbolic system.

Description
Keywords
generalized stochastic process, gaussian process, white noise, hyperbolic system, wave-equation, white noise, dimensions, mathematics, applied
Citation
Kim, J. U., "On a stochastic hyperbolic system in linear elasticity," SIAM J. Math. Anal., 32(2), 304-322, (2000). DOI: 10.1137/s0036141099350377