Events
DMS Stochastic Analysis Seminar |
Time: Nov 02, 2021 (12:00 PM) |
Location: 326 Parker Hall and ZOOM |
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 Lp(Ω)-solution exists for all p≥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, T2, before which a unique L2(Ω)-solution exists, but after which the series corresponding to the L2(Ω) 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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