Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise

Abstract: In this article, we study the global well-posedness of hyperbolic SPDEs on a bounded domain in $\mathbb{R}^d$, driven by a space-time Lévy white noise, where the drift and diffusion coefficients are assumed to be locally Lipschitz with at most linear growth. The equations are driven by two types of space-time Lévy noise: (i) a finite-variance Lévy white noise, and (ii) a symmetric Lévy basis that may have infinite variance. A typical example of the second class is the symmetric $α$-stable (S$α$S) random measure with $α\in (0,2)$.