STOCHASTIC WAVE EQUATIONS WITH CUBIC NONLINEARITIES IN TWO DIMENSIONS By

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 coefficients. 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 Lp-growth, and almost sure exponential sta-bility. The main tool is the study of related Lyapunov-type functionals which admits t