Stochastic Wave Equations With Cubic Nonlinearities in Two Dimensions

<p>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.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2012

Author dc:creator

• Hazaimeh, Haziem Mohammad

Contributors dc:contributor

• Hazaimeh, Haziem

Repository record dc:identifier

https://opensiuc.lib.siu.edu/dissertations/471

OAI identifier oai:identifier

oai:opensiuc.lib.siu.edu:dissertations-1471