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

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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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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Mathematics Subject Classification (2000):

  • 60H15

Key words:

  • Stochastic hyperbolic equations
  • homogeneous Wiener process