| Abstract: |
| Semi-linear wave equations with power-law nonlinearities and Q-regular
space-time white noise on rectangular domains are considered both analytically and numerically.
These SPDEs describe the displacement of noisy strings or membranes in mechanical
engineering, laser dynamics or chemical processes. We discuss their analysis
by the eigenfunction approach allowing us to truncate the corresponding
infinite-dimensional stochastic systems, to control its error, energy,
existence, uniqueness and stability. The truncated system of ordinary SDEs
is numerically integrated by partial-implicit, midpoint-based difference
methods. These nonstandard methods control the growth of related mean energy
functional with time $t$. To understand the qualitative behavior of both
analytical solutions and numerical approximations, we investigate the
existence and uniqueness of approximative strong solutions using energy-type methods
(i.e. by Lyapunov-type functionals). |
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