Caltech/UCLA/USC Joint Analysis Seminar
Caltech, 310 Linde Hall
Physical systems are often idealized as being isolated because very distant events ought not have a significant influence. Mathematically, this often translates to solving problems with localized data. In this talk, I will discuss results which make this intuitive idealization rigorous. Indeed, we study the effects that distant perturbations have on solutions to nonlinear wave equations. We prove a stability statement, which requires analyzing the spacetime geometry of the interaction of waves originating from distant sources. I also hope to describe some of the additional difficulties involved in extending these results to the physically interesting case of the Einstein vacuum equations of general relativity. This is joint work with Federico Pasqualotto (Duke University).