Author ORCID Identifier
Year of Publication
Doctor of Philosophy (PhD)
Arts and Sciences
Dr. Mihai Tohaneanu
We investigate the asymptotic behaviour of solutions to a range of linear and nonlinear hyperbolic equations on asymptotically flat spacetimes. We develop a comprehensive framework for the analysis of pointwise decay of linear and nonlinear wave equations on asymptotically flat manifolds of three space dimensions that are allowed to be time-varying or nonstationary, including quasilinear wave equations. The Minkowski space and time-varying perturbations thereof are included among these spacetimes. A result on scattering for a nonlinear wave equation with finite-energy solutions on nonstationary spacetimes is presented. This work was motivated in part by the investigation of more precise asymptotic behaviour for dispersive equations.
Digital Object Identifier (DOI)
Looi, Shi-Zhuo, "Asymptotic behaviour of hyperbolic partial differential equations" (2023). Theses and Dissertations--Mathematics. 101.