Weak solutions to stochastic wave equations with values in Riemannian manifolds

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Publication details

Journal Communications in Partial Differential Equations
DatePublished - Sep 2011
Issue number9
Volume36
Number of pages30
Pages (from-to)1624-1653
Original languageEnglish

Abstract

Let M be a compact Riemannian manifold. We prove existence of a global
weak solution of the stochastic wave equation Dt@tu = Dx@xu + (Xu + ¸0(u)@tu +
¸1(u)@xu) ¿W where X is a continuous tangent vector field on M, ¸0, ¸1 are continuous vector bundles homomorphisms from TM to TM and W is a spatially homogeneous Wiener process on R with finite spectral measure. A new general method of constructing weak solutions of SPDEs that does not rely on martingale representation theorem is used.

    Research areas

  • stochastic wave equation; , geometric wave equation.

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