Events
DMS Stochastic Analysis Seminar |
| Time: Nov 02, 2021 (12:00 PM) |
| Location: 326 Parker Hall and ZOOM |
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Details: Speaker: Nicholas Eisenberg (Auburn) Title: Interpolating the stochastic heat and wave equations with time-independent noise
Abstract: In this talk, I will present a recent joint-work with Dr. Le Chen, where we study a class of stochastic partial differential equations with fractional differential operators subject to some time-independent multiplicative Gaussian noise. We derive sharp conditions, under which a unique global \(L^p\)(\(\Omega\))-solution exists for all \(p \ge 2\). In this case, we derive exact moment asymptotics following the same strategy in a recent work by Balan et al [1]. In the case when there exists only a local solution, we determine the precise deterministic time, \(T_2\), before which a unique \(L^2\)(\(\Omega\))-solution exists, but after which the series corresponding to the \(L^2\)(\(\Omega\)) moment of the solution blows up. By properly choosing the parameters, results in this paper interpolate the known results for both stochastic heat and wave equations.
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