COSAM » Events » 2021 » November » DMS Stochastic Analysis Seminar

 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 $$L^p$$($$\Omega$$)-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.

Last updated: 11/01/2021