Remarks on non-linear noise excitability of some stochastic heat equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Foondun, Mohammud¹  Joseph, Mathew² 

[1] Univ Loughborough, Loughborough, Leics, England

[2] Univ Sheffield, Sheffield S10 2TN, S Yorkshire, England

关键词: Stochastic partial differential equations;   

DOI  :  10.1016/j.spa.2014.04.015

来源: Elsevier

【 摘 要 】

We consider nonlinear parabolic SPDEs of the form at partial derivative(t)u = Delta u + lambda sigma(u) (w) over dot on the interval (0, L), where (w) over dot denotes space time white noise, sigma is Lipschitz continuous. Under Dirichlet boundary conditions and a linear growth condition on sigma, we show that the expected L-2-energy is of order exp[const x lambda(4)] as lambda -> infinity. This significantly improves a recent result of Khoshnevisan and Kim Our method is very different from theirs and it allows us to arrive at the same conclusion for the same equation but with Neumann boundary condition. This improves over another result in Khoshnevisan and Kim. (C) 2014 The Authors. Published by Elsevier B.V.

【 授权许可】

Free