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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Hazaimeh, Haziem Mohammad"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Open Access Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hazaimeh, Haziem"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-01T07:00:00Z","date_published":"2012-05-01T07:00:00Z","updated_at":"2026-07-24T04:33:54Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/471","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hazaimeh, Haziem"]},{"key":"dc:creator","label":"Author","values":["Hazaimeh, Haziem Mohammad"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2012-05-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/471"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Stochastic Wave Equations With Cubic Nonlinearities in Two Dimensions"]}]}],"canonical_facts":{"dc:contributor":["Hazaimeh, Haziem"],"dc:creator":["Hazaimeh, Haziem Mohammad"],"dc:date.available":["2012-05-01T07:00:00Z"],"dc:description.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.
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