Stability and Mean Consistent of Fourier Solutions of Nonlinear Stochastic Heat Equations in 1D

Haziem M. Hazaimeh

doi:https://doi.org/10.14445/22315373/IJMTT-V65I10P502

International Journal of Mathematics Trends and Technology

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Volume 65 | Issue 10 | Year 2019 | Article Id. IJMTT-V65I10P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I10P502

Stability and Mean Consistent of Fourier Solutions of Nonlinear Stochastic Heat Equations in 1D

Haziem M. Hazaimeh

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. Also, We prove that the Fourier coefficient solution is mean consistent. The main tool is the study of re- lated 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.

Keywords

Nonlinear stochastic heat equation, Fourier solution, Stability, Mean Consistent.

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Citation :

Haziem M. Hazaimeh, "Stability and Mean Consistent of Fourier Solutions of Nonlinear Stochastic Heat Equations in 1D," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 10, pp. 5-14, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I10P502