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Transactions of the American Mathematical Society

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On a stochastic wave equation with unilateral boundary conditions

Author: Jong Uhn Kim
Journal: Trans. Amer. Math. Soc. 360 (2008), 575-607
MSC (2000): Primary 35L65, 35R60, 60H15
Published electronically: July 20, 2007
MathSciNet review: 2346463
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Abstract: We prove the existence and uniqueness of solutions to the initial boundary value problem for a one-dimensional wave equation with unilateral boundary conditions and random noise. We also establish the existence of an invariant measure.

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Additional Information

Jong Uhn Kim
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123

Keywords: Unilateral boundary conditions, Brownian motion, existence of a solution, pathwise uniqueness, invariant measure, probability distribution.
Received by editor(s): June 9, 2004
Received by editor(s) in revised form: July 17, 2005
Published electronically: July 20, 2007
Article copyright: © Copyright 2007 American Mathematical Society