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Georgia Southern University

Fourier Analysis of Wave Equations

Abstract

dc:description.abstract

<p>Partial Differential Equation is one of the major influential and useful subjects in Mathematical Sciences. In this thesis, I mainly use Fourier analysis and PDE methods to study the solution to an inhomogeneous wave equation on Euclidean spaces. I obtained the existence, uniqueness, and regularity for the solution. In the classical case, the datum involved is required to have up to C2 smoothness; my results treat the low regularity case and only require Hs smoothness with fractional order s. The main tools include Fourier transform, Duhamel principle, and the method of energy estimates. The results have potential applications to the solutions of nonlinear wave equations with low regularity datum, which have background and implications in Physics and Engineering.</p>

Degree

thesis:*
Name thesis:degree_name
Master of Science in Mathematics (M.S.)
Level thesis:degree_level
Thesis (restricted to Georgia Southern)
Discipline thesis:degree_discipline
Department of Mathematical Sciences
Year dc:date.available
2010

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Uchida, Masahiko
Contributors dc:contributor
  • Sze-Man Ngai
  • Alex Stokolos
  • Yan Wu

Subjects

dc:subject × 5

Identifiers

dc:identifier.*
Repository record dc:identifier
https://digitalcommons.georgiasouthern.edu/etd/684
OAI identifier oai:identifier
oai:digitalcommons.georgiasouthern.edu:etd-1684

Chain of custody

source
Harvested from
Georgia Southern University
Base URL
digitalcommons.georgiasouthern.edu/do/oai/
Last updated
2026-07-24
Source record
OAI-PMH GetRecord
citation

Uchida, Masahiko. Fourier Analysis of Wave Equations. Thesis (restricted to Georgia Southern) thesis, 2010. https://digitalcommons.georgiasouthern.edu/etd/684