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, when the drift and diffusion coefficients are locally Lipschitz and have linear growth. The equations are driven by two types of space-time Lévy noise: (i) a finite-variance Lévy white noise; or (ii) a symmetric Lévy basis that may have infinite variance. A typical example of noise of the second type is the symmetric $\hat{I}\pm$-stable (S$\hat{I}\pm$S) random measure with $\hat{I}\pm \in (0,2)$.

42 pages