Effects of the noise level on stochastic fractional heat equations

2016/04/28 by Kexue Li, Li, Kexue
Economics, Econometrics and Finance · Mathematics · Computer Science · #Stochastic processes and financial applications #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1604.08341

Abstract

We consider the stochastic fractional heat equation ∂_tu=\triangle^α/2u+λσ(u)w on [0,L] with Dirichlet boundary conditions, where w denotes the space-time white noise. For any λ>0, we prove that the pth moment of sup_{x∈ [0,L]}|u(t,x)| grows at most exponentially. Moreover, we prove that the pth moment of sup_{x∈ [0,L]}|u(t,x)| is exponentially stable if λ is small. At last, We obtain the noise excitation index of pth energy of u(t,x) as λ→ ∞.

Citations

• Some theorems on stable processes

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