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Strong solutions to stochastic wave equations with values in Riemannian manifolds

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JournalJournal of Functional Analysis
DatePublished - 15 Dec 2007
Issue number2
Volume253
Number of pages33
Pages (from-to)449-481
Original languageEnglish

Abstract

Let M be a d-dimensional compact Riemannian manifold. We prove existence of a unique global strong solution of the stochastic wave equation D-t partial derivative(t)u = D-x partial derivative(x)u + Y-u (partial derivative(t)u, partial derivative(x)u) V, where Y is a C-1-smooth transformation and W is a spatially homogeneous Wiener process on R whose spectral measure has finite moments up to order 2. (c) 2007 Published by Elsevier Inc.

    Research areas

  • stochastic wave equation, geometric wave equation, HOMOGENEOUS WIENER PROCESS, WEAK SOLUTIONS, CAUCHY-PROBLEM, EVOLUTION-EQUATIONS, HARMONIC MAPS, SINGULARITIES, EXISTENCE, DRIVEN, SPACE, SMOOTHNESS

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