Date of Award

May 2017

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Hans Volkmer

Committee Members

Dashan Fan, Peter Hinow, Lijing Sun, Bruce Wade


The Fourier transform, F, on R^N (N≥1) transforms the Cauchy problem for the strongly damped wave equation u_tt(t,x) - Δu_t(t,x) - Δu(t,x) = 0 to an ordinary differential equation in time t. We let u(t,x) be the solution of the problem given by the Fourier transform, and v(t,ƺ) be the asymptotic profile of F(u)(t,ƺ) = û(t,ƺ) found by Ikehata in [4].

In this thesis we study the asymptotic expansions of the squared L^2-norms of u(t,x), û(t,ƺ) - v(t,ƺ), and v(t,ƺ) as t → ∞. With suitable initial data u(0,x) and u_t(0,x), we establish the rate of growth or decay of the squared L2-norms of u(t,x) and v(t,ƺ) as t → ∞. By noting the cancellation of leading terms of their respective expansions, we conclude that the rate of convergence between û(t,ƺ) and v(t,ƺ) in the L^2-norm occurs quickly relative to their individual behaviors. Finally we consider three examples in order to illustrate the results.