Abstract

In this paper, we obtain the existence and uniqueness of the strong solution to one (spatial) dimensional stochastic wave equation ∂2u(t,x)∂t2=∂2u(t,x)∂x2+σ(t,x,u(t,x))W˙(t,x) assuming σ(t,x,0)=0, where W˙ is a mean zero Gaussian noise which is white in time and fractional in space with Hurst parameter H∈(1/4,1/2).

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