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

[摘要] 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.

[关键词] Nonlinear stochastic heat equation;Additive spacetime noise;Lyapunov functional;Fourier solution;Finite dimensional approximations;Moments;Stability