Nonlinear stochastic wave Equation driven by rough noise

2021/10/26 by Liu, Shuhui, Hu, Yaozhong, Wang, Xiong · 1 citation
#60H07 #65M80 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 60H15 #Probability (math.PR) #secondary 60H05

paper · doi:10.48550/arxiv.2110.13800

Abstract

In this paper, we obtain the existence and uniqueness of the strong solution to one spatial dimension stochastic wave equation (∂² u(t,x))/(∂ t²)=(∂² u(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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• Growth rates for the Hölder coefficients of the linear stochastic fractional heat equation with rough dependence in space

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