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Nonlinear stochastic wave equation driven by rough noise

Shuhui Liu,Yaozhong Hu,Xiong Wang

Journal of Differential Equations（2022）

Cited 2|Views2
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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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Key words
Rough fractional noise,Stochastic wave equation,Decomposition of wave kernel,Sup Lp-norm,Well-posedness,Hölder continuity
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