Zeitschrift für Angewandte und Computermathematik

Stability of Fourier Solutions of Nonlinear Stochastic Heat Equations in 1D

Abstract

Hazaimeh MH

The main focus of this article is studying the stability of solutions of nonlinear stochastic heat equation and give conclusions in two cases: stability in probability and almost sure exponential stability. The main tool is the study of related Lyapunov-type functionals. The analysis is carried out by a natural N-dimensional truncation in isometric Hilbert spaces and uniform estimation of moments with respect to N.

Nonlinear stochastic heat equation, additive space-time noise, Lyapunov functional, Fourier solution, finitedimensional approximations, moments, stability.