Conservation laws with a random source

Conservation laws with a random source We study the scalar conservation law with a noisy nonlinear source, namely, u l + f(u) x = h(u, x, t) + g(u)W(t), where W(t) is the white noise in the time variable, and we analyse the Cauchy problem for this equation where the initial data are assumed to be deterministic. A method is proposed to construct approximate weak solutions, and we then show that this yields a convergent sequence. This sequence converges to a (pathwise) solution of the Cauchy problem. The equation can be considered as a model of deterministic driven phase transitions with a random perturbation in a system of two constituents. Finally we show some numerical results motivated by two-phase flow in porous media. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Conservation laws with a random source

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Publisher
Springer-Verlag
Copyright
Copyright © 1997 by Springer-Verlag New York Inc.
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02683344
Publisher site
See Article on Publisher Site

Abstract

We study the scalar conservation law with a noisy nonlinear source, namely, u l + f(u) x = h(u, x, t) + g(u)W(t), where W(t) is the white noise in the time variable, and we analyse the Cauchy problem for this equation where the initial data are assumed to be deterministic. A method is proposed to construct approximate weak solutions, and we then show that this yields a convergent sequence. This sequence converges to a (pathwise) solution of the Cauchy problem. The equation can be considered as a model of deterministic driven phase transitions with a random perturbation in a system of two constituents. Finally we show some numerical results motivated by two-phase flow in porous media.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Sep 1, 1997

References

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