Date of Award

12-1-2014

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Schurz, Henri

Abstract

The main focus of my dissertation is the Modified Stochastic Sine-Gordon Equation: utt = 2uxx − ut − sin(|u|^(&gamma)) + b(u, du/dt)dW/dt where &gamma > 0 is the parameter of the power of non-linearity, &delta &ge 0 is the magnitude of non-linearity, &alpha> 0 be the damping parameter, and &sigma the diffusion intensity, on one dimensional domain. We analyze the properties of the solution of the SPDE by the eigenfunctions approach allowing us to truncate the infinite-dimensional stochastic system (i.e the SDEs of Fourier coefficients related to the SPDE), to control its energy, existence, uniqueness, continuity and stability. The analysis relies on the investigation of expected Lyapunov functional of the energy in terms of all system-parameters. We simulate the model with respect to all system-parameters to visualize our conclusions.

Share

COinS
 

Access

This dissertation is only available for download to the SIUC community. Others should contact the
interlibrary loan department of your local library or contact ProQuest's Dissertation Express service.