Events
Stochastics Seminar |
| Time: Mar 10, 2016 (02:00 PM) |
| Location: Parker Hall 322 |
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Details: Speaker: Dr. Erkan Nane
Title: On the behavior of stochastic heat equations on bounded domains
Abstract: Consider the following equation
\( ∂tut(x) = ∂xxut(x) + λσ(ut(x))F˙ (t, x)\)
on an interval. Under Dirichlet boundary condition, we show that in the long run, the second moment of the solution grows exponentially if \(λ\) is large enough. But if \(λ\) is small, then the second moment eventually decays exponentially. If the Dirichlet boundary condition is replaced by the Neumann one, then the second moment grows exponentially fast for all \(λ\) positive. We also give some preliminary extensions of these results to other space-time settings.
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