Moment bounds for stochastic wave equation with spatially inhomogeneous white noise

In this paper, we consider the one-dimensional stochastic wave equation with spatially inhomogeneous white noise \frac\partial^2\partial t^2 u(t, x)=\frac\partial^2\partial x^2 u(t, x)+\sigma(u(t, x)) \frac\partial^2\partial t \partial x w_\mu(t, x). Under some mild assumptions on the catalytic measure of the inhomogeneous Brownian sheet, we prove that the existence, uniqueness and Hölder continuity of the solution in some Banach space. Moreover we also establish the upper and lower moment bounds for the solution. As a by-product, we prove that the solution is weakly full intermittent based on the moment bounds.