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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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
Mathematics Subject Classification (2000):
- Stochastic hyperbolic equations
- homogeneous Wiener process