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On a stochastic wave equation driven by a non-Gaussian Lévy process. (English) Zbl 1196.60113
The authors study a hyperbolic equation with a non-Gaussian noise perturbation. The existence, uniqueness and asymptotic behaviour of the weak solutions to white-noise perturbed stochastic wave equations have been investigated by several authors. Specially, Peszat and Zabczyk considered the following wave equation driven by an impulsive noise: $\frac{\partial^2u(t)}{\partial t^2}= [\Delta u(t) + f(u(t))]dt + b(u(t))PdZ(t)$ where $$f, b$$ are Lipschitz continuous real functions, $$P$$ is a regularizing linear operator, and the impulsive noise $$Z_t$$ is formulated as a Poisson random measure. Comparing with this work, the authors’ objective is first to consider the more general damped wave equation which is used to model nonlinear phenomena in relativistic quantum mechanics. Their focus is on the notion of weak solution which is stronger than the mild solution. Moreover, the perturbation can inculde a general non-Gaussian Lévy noise. The existence of a unique invariant measure is also explored.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35K90 Abstract parabolic equations 47D07 Markov semigroups and applications to diffusion processes 35R30 Inverse problems for PDEs
##### Keywords:
Damped wave equation; Levy noise; Invariant measure
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##### References:
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