Date of Award
5-1-2012
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Hazaimeh, Haziem
Abstract
The main focus of my dissertation is the qualitative and quantative behavior of stochastic Wave equations with cubic nonlinearities in two dimensions. I evaluated the stochastic nonlinear wave equation in terms of its Fourier coecients. I proved that the strong solution of that equation exists and is unique on an appropriate Hilbert space. Also, I studied the stability of N-dimensional truncations and give conclusions in three cases: stability in probability, estimates of L^p-growth, and almost sure exponential stability. The main tool is the study of related Lyapunov-type functionals which admits to control the total energy of randomly vibrating membranes. Finally, I studied numerical methods for the Fourier coecients. I focussed on the linear-implicit Euler method and the linear-implicit mid-point method. Their schemes have explicit representations. Eventually, I investigated their mean consistency and mean square consistency.
Access
This dissertation is Open Access and may be downloaded by anyone.