Some effects of the noise intensity upon non-linear stochastic heat equations on [0,1]

2015/06/19 by Xie, Bin
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1506.05954

Abstract

Various effects of the noise intensity upon the solution u(t,x) of the stochastic heat equation with Dirichlet boundary conditions on [0,1] are investigated. We show that for small noise intensity, the p-th moment of sup_{x ∈ [0,1]} |u(t,x)| is exponentially stable, however, for large one, it grows at least exponentially. We also prove that the noise excitation of the p-th energy of u(t,x) is 4, as the noise intensity goes to infinity. We formulate a common method to investigate the lower bounds of the above two different behaviors for large noise intensity, which are hard parts in \citeFoJo-14, \citeFoNu and \citeKhKi-15.

Related

• Effects of the noise level on stochastic fractional heat equations
• Non-linear noise excitation and intermittency under high disorder
• The effect of noise intensity on stochastic parabolic equations
• Remarks on non-linear noise excitability of some stochastic heat equations
• The compact support property for solutions to stochastic heat equations with stable noise