## Differential and Integral Equations

### Time decay of solution for the KdV equation with multiplicative space-time noise

Yoshio Tsutsumi

#### Abstract

We consider the asymptotic behavior in large time of solutions for the KdV equation with multiplicative space-time noise. Under certain assumptions on the noise, we prove that the $L^2$ norm of solutions almost surely decays to zero as time goes to infinity. This phenomena is called stabilization by noise.

#### Article information

Source
Differential Integral Equations, Volume 21, Number 9-10 (2008), 959-970.

Dates
First available in Project Euclid: 20 December 2012