One-Dimensional Nonlinear Stochastic Wave Equation and Triviality Effect

Abstract

The limiting behavior of solutions to stochastic wave equations with singularities represented by stochastic terms is considered. In cases when the initial data are certain functionals of the smoothed white noise process, it is proved that the triviality effect appears. At the end of the paper, a concrete application of the smoothed positive noise is given.

Keywords:

• Generalized solutions
• Generalized stochastic processes
• Nonlinear stochastic wave equation

Mathematics Subject Classification:

• 35R60
• 60H15

ACKNOWLEDGMENT

The author would like to express gratitude to Michael Oberguggenberger for his interest and many valuable suggestions for improvement. The paper was supported by the Serbian Ministry of Science, Project 144016.