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Stabilization of partial differential equations by noise

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  • Kwiecinska, Anna A.

Abstract

We provide an example of a class of partial differential equations being stabilized (in terms of Lyapunov exponents) by noise. In particular, we show that the stability of the heat equation can be improved by adding a stochastic term to the equation. We also give an example of an unstable PDE made stable by noise.

Suggested Citation

  • Kwiecinska, Anna A., 1999. "Stabilization of partial differential equations by noise," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 179-184, February.
    • Handle: RePEc:eee:spapps:v:79:y:1999:i:2:p:179-184
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    Cited by:

    1. Siqueira, Adriano F. & Peixoto, Carlos J.T. & Wu, Chen & Qian, Wei-Liang, 2016. "Effect of stochastic transition in the fundamental diagram of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 1-13.
    2. Ruofeng Rao & Shouming Zhong, 2017. "Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory," Complexity, Hindawi, vol. 2017, pages 1-9, September.
    3. Rößler, Andreas & Seaïd, Mohammed & Zahri, Mostafa, 2009. "Numerical simulation of stochastic replicator models in catalyzed RNA-like polymers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3577-3586.
    4. Qian, Wei-Liang & F. Siqueira, Adriano & F. Machado, Romuel & Lin, Kai & Grant, Ted W., 2017. "Dynamical capacity drop in a nonlinear stochastic traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 328-339.

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