Article ID Journal Published Year Pages File Type
10527199 Stochastic Processes and their Applications 2014 12 Pages PDF
Abstract
We consider nonlinear parabolic SPDEs of the form ∂tu=Δu+λσ(u)ẇ on the interval (0,L), where ẇ denotes space-time white noise, σ is Lipschitz continuous. Under Dirichlet boundary conditions and a linear growth condition on σ, we show that the expected L2-energy is of order exp[const×λ4] as λ→∞. 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.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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