Differential and Integral Equations
- Differential Integral Equations
- Volume 21, Number 9-10 (2008), 959-970.
Time decay of solution for the KdV equation with multiplicative space-time noise
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.
Differential Integral Equations, Volume 21, Number 9-10 (2008), 959-970.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H15: Stochastic partial differential equations [See also 35R60]
Tsutsumi, Yoshio. Time decay of solution for the KdV equation with multiplicative space-time noise. Differential Integral Equations 21 (2008), no. 9-10, 959--970. https://projecteuclid.org/euclid.die/1356038594