Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time L\'evy 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 L\'evy white noise, when the drift and diffusion coefficients are locally Lipschitz and have linear growth. The equations are driven by two types of space-time L\'evy noise: (i) a finite-variance L\'evy white noise; or (ii) a symmetric L\'evy basis that may have infinite variance. A typical example of noise of the second type is the symmetric $\alpha$-stable (S$\alpha$S) random measure with $\alpha \in (0,2)$.