Nonlinear stochastic wave Equation driven by rough noise

Abstract

In this paper, we obtain the existence and uniqueness of the strong solution to one spatial dimension stochastic wave equation $\frac{{\partial }^{2}u(t,x)}{\partial t^2}=\frac{{\partial }^{2}u(t,x)}{\partial x^2}+\sigma (t,x,u(t,x))\dot{W}(t,x)$ assuming $\sigma (t,x,0)=0$, where $\dot{W}$ is a mean zero Gaussian noise which is white in time and fractional in space with Hurst parameter $H\in (1/4,1/2)$.

49 pages