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Existence of global mild and strong solutions to stochastic hyperbolic evolution equations driven by a spatially homogeneous Wiener process

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Abstract

Semilinear second order stochastic hyperbolic equations driven by a spatially homogeneous Wiener process are studied. Sufficient conditions in terms of Lyapunov functions for the equation to have global mild or strong solutions are found. In particular, the results apply to equations with polynomial drift and diffusion coefficients.

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Authors and Affiliations

  1. Institut Élie Cartan, Université Henri Poincaré Nancy 1, Vandoeuvre-lès-Nancy, France

    Martin Ondreját

  2. Mathematical Institute AS CR, Žitná 25, 115 67, Praha 1, Czech Republic

    Martin Ondreját

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  1. Martin Ondreját
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Correspondence to Martin Ondreját.

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Ondreját, M. Existence of global mild and strong solutions to stochastic hyperbolic evolution equations driven by a spatially homogeneous Wiener process. J.evol.equ. 4, 169–191 (2004). https://doi.org/10.1007/s00028-003-0130-y

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  • DOI: https://doi.org/10.1007/s00028-003-0130-y

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