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Exact solvability and moment asymptotic of SPDEs with time-independent noise by Professor Le Chen

This is a past event.

Friday, March 25 at 4:00pm to 5:00pm

Virtual Event

Please welcome Professor Le Chen from the Department of Mathematics and Statistics at Auburn University.

Abstract: In this talk, I will report a joint work with Raluca Balan and Xia Chen [BCC22]
and a following-up work [CE22] with Nicholas Eisenberg. In this line of research, we
first study the stochastic wave equation in dimensions d ≤ 3, driven by a Gaussian noise
W ̇ which does not depend on time. We assume that the spatial noise is either white,
or the covariance functional of the noise satisfies a scaling property similar to the Riesz
kernel. The solution is interpreted in the Skorohod sense using Malliavin calculus. We
obtain the exact asymptotic behaviour of the p-th moment of the solution when either
the time or p goes to infinity. For the critical case, namely, when d = 3 and the spatial
noise is white, we obtain the exact transition time for the second moment to be finite.
The main obstacle for this work is the lack of the Feynman-Kac representation for the
moment, which has been overcome by a careful analysis of the Wiener chaos expansion.
Our methods turn out to be very general and can be applied to a broad class of SPDEs,
which include stochastic heat and wave equations as two special cases.

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Meeting ID: 930 5388 4755

Passcode: AAM2022

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Department of Mathematics and Statistics
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