Noise and stability in reaction-diffusion equations

Guangying Lv; Jinlong Wei; Guang-an Zou

doi:10.3934/mcrf.2021005

Article Contents

2022, Volume 12, Issue 1: 147-168. Doi: 10.3934/mcrf.2021005

This issue Previous Article Model reduction for fractional elliptic problems using Kato's formula Next Article Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback

Noise and stability in reaction-diffusion equations

1.
College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
3.
Institute of Applied Mathematics, Henan University, Kaifeng 475001, China

^* Corresponding author: Jinlong Wei
^* Corresponding author: Jinlong Wei

Received: August 2020

Revised: November 2020

Early access: March 2021

Published: March 2022

The authors are grateful to the referees for their valuable suggestions and comments on the original manuscript. This research was partly supported by the NSF of China grants 11771123, 11501577, 11626085 and the Startup Foundation for Introducing Talent of NUIST

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Abstract

We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is firstly established. Then, by using the Lyapunov method, sufficient conditions for mean square and stochastic stability are given. The results show that the multiplicative noise can make the solution stable, but the additive noise will be not.

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Mathematics Subject Classification: Primary: 35B35; Secondary: 60H15.

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