Term of Award

Fall 2010

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Department

Department of Mathematical Sciences

Committee Chair

Shijun Zheng

Committee Member 1

Sze-Man Ngai

Committee Member 2

Alex Stokolos

Committee Member 3

Yan Wu

Abstract

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.

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