TY - JOUR
T1 - Remarks on non-linear noise excitability of some stochastic heat equations
AU - Foondun, Mohammud
AU - Joseph, Mathew
PY - 2014/5/13
Y1 - 2014/5/13
N2 - 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.
AB - 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.
KW - Stochastic partial differential equations
KW - Neumann boundary condition
UR - http://www.scopus.com/inward/record.url?scp=84902667433&partnerID=8YFLogxK
UR - http://www.sciencedirect.com/science/journal/03044149
U2 - 10.1016/j.spa.2014.04.015
DO - 10.1016/j.spa.2014.04.015
M3 - Article
AN - SCOPUS:84902667433
SN - 0304-4149
VL - 124
SP - 3429
EP - 3440
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 10
ER -
