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A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel

Published online by Cambridge University Press:  20 November 2018

C. Mueller
C. Mueller*
Affiliation:
Department of Mathematics University of Rochester Rochester, New York 14627 U.S.A.
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Abstract

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We give a modulus of continuity for solutions of the wave equation with a noise term:

utt = Δu + a(u) + b(u)G, x ∈ ℝ3

where G is a Gaussian noise. This case is more difficult than in lower dimensions because the fundamental solution of the wave equation is singular.

Keywords

60H1535R6035L05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 6 , 01 December 1993 , pp. 1263 - 1275
Copyright
Copyright © Canadian Mathematical Society 1993

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