Abstract
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.
Highlights
In this article we study the stability of solutions of semi-linear stochastic heat equations ut = σ 2∆u + A(u)B(u) dW dt with cubic nonlinearities A(u) in one dimensions in terms of all systems parameters, i.e., with non-global Lipschitz continuous nonlinearities
In this article we study the stability of solutions of semi-linear stochastic heat equations ut dW dt with cubic nonlinearities A(u) in one dimensions in terms of all systems parameters, i.e., with non-global Lipschitz continuous nonlinearities
Some authors study the stability of stochastic heat equations like Fournier and Printems [6] study the stability of the mild solution
Summary
In this article we study the stability of solutions of semi-linear stochastic heat equations ut. Many authors have treated stochastic heat equations [1,2]), semi-linear stochastic heat equations Some authors study the stability of stochastic heat equations like Fournier and Printems [6] study the stability of the mild solution. Walsh reats the stochastic heat equations in one dimension. Chow [1] studies that the null solution of the stochastic heat equation is stable in probability by using the definition.
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