On the well-posedness of the Mortensen observer for a defocusing cubic wave equation

PDE Seminar
Tuesday, February 27, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Online: https://gatech.zoom.us/j/95574359880?pwd=cGpCa3J1MFRkY0RUeU1xVFJRV0x3dz09
Jesper Schröder – Technische Universität Berlin – jschroed@math.tu-berlin.dehttps://www.tu.berlin/en/fgmso/jesper-schroeder
Lukas Wessels

In this presentation the analytical background of nonlinear observers based on minimal energy estimation is discussed. Originally, such strategies were proposed for the reconstruction of the state of finite dimensional dynamical systems by means of a measured output where both the dynamics and the output are subject to white noise. Our work aims at lifting this concept to a class of partial differential equations featuring deterministic perturbations using the example of a wave equation with a cubic defocusing term in three space dimensions. In particular, we discuss local regularity of the corresponding value function and consider operator Riccati equations to characterize its second spatial derivative.