Joint USYD and UNSW Seminar on Stochastic PDEs: Justin Forlano (Monash) -- Quasi-invariance of the Gaussian measure for a stochastic nonlinear damped wave equation

Zoom:  
https://uni-sydney.zoom.us/j/87298194391?pwd=6hXoOgkwXLxKN09Brm0PulUFGg7Kbf.1
Meeting ID: 872 9819 4391
Password: 856583

We consider the stochastic damped nonlinear wave equation in two dimensions.  We show
that, in the entire non-singular regime, the law of the solution remains absolutely
continuous with respect to the law of the solution to the linear stochastic damped wave
equation.  Whilst such results are typically well-known for stochastic parabolic
equations, the associated techniques fail in the hyperbolic setting at low-regularity.
Our argument extends to the stochastic setting recent ideas in the study of the
quasi-invariance of Gaussian measures under the flow of Hamiltonian PDEs.  This talk is
based on joint work with L.  Tolomeo (University of Edinburgh).