Author ORCID Identifier
Date Available
5-10-2023
Year of Publication
2023
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. Mihai Tohaneanu
Abstract
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)
https://doi.org/10.13023/etd.2023.206
Recommended Citation
Looi, Shi-Zhuo, "Asymptotic behaviour of hyperbolic partial differential equations" (2023). Theses and Dissertations--Mathematics. 101.
https://uknowledge.uky.edu/math_etds/101
