Nonlinear stochastic wave equation driven by rough noise

In this paper, we obtain the existence and uniqueness of the strong solution to one spatial dimension stochastic wave equation ∂ u(t,x) ∂t2 = ∂u(t,x) ∂x2 + σ(t, x, u(t, x))Ẇ (t, x) assuming σ(t, x, 0) = 0, where Ẇ 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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