Modified Stochastic Sine-Gordon Equation

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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Campus Only Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2014

Author dc:creator

• Talafha, Abdallah M.

Contributors dc:contributor

• Schurz, Henri

• Fourier solutions
• Lyapunov functions
• MODIFIED STOCHASTIC SINE-GORDON EQUATION
• Q-regular space-time noise
• total energy functional
• trace formula

Repository record dc:identifier

https://opensiuc.lib.siu.edu/dissertations/973

OAI identifier oai:identifier

oai:opensiuc.lib.siu.edu:dissertations-1977