Research output: Contribution to journal › Article

**Weak solutions to stochastic wave equations with values in Riemannian manifolds.** / Brzezniak, Zdzislaw; Ondreját, Martin.

Research output: Contribution to journal › Article

Brzezniak, Z & Ondreját, M 2011, 'Weak solutions to stochastic wave equations with values in Riemannian manifolds', * Communications in Partial Differential Equations *, vol. 36, no. 9, pp. 1624-1653. https://doi.org/10.1080/03605302.2011.574243

Brzezniak, Z., & Ondreját, M. (2011). Weak solutions to stochastic wave equations with values in Riemannian manifolds. * Communications in Partial Differential Equations *, *36*(9), 1624-1653. https://doi.org/10.1080/03605302.2011.574243

Brzezniak Z, Ondreját M. Weak solutions to stochastic wave equations with values in Riemannian manifolds. Communications in Partial Differential Equations . 2011 Sep;36(9):1624-1653. https://doi.org/10.1080/03605302.2011.574243

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title = "Weak solutions to stochastic wave equations with values in Riemannian manifolds",

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.",

keywords = "stochastic wave equation; , geometric wave equation.",

author = "Zdzislaw Brzezniak and Martin Ondrej{\'a}t",

year = "2011",

month = "9",

doi = "10.1080/03605302.2011.574243",

language = "English",

volume = "36",

pages = "1624--1653",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "9",

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T1 - Weak solutions to stochastic wave equations with values in Riemannian manifolds

AU - Brzezniak, Zdzislaw

AU - Ondreját, Martin

PY - 2011/9

Y1 - 2011/9

N2 - 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.

AB - 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.

KW - stochastic wave equation;

KW - geometric wave equation.

U2 - 10.1080/03605302.2011.574243

DO - 10.1080/03605302.2011.574243

M3 - Article

VL - 36

SP - 1624

EP - 1653

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 9

ER -