论文标题
反应扩散方程中的噪声和稳定性
Noise and Stability in Reaction-diffusion Equations
论文作者
论文摘要
我们研究了存在噪声时反应扩散方程的稳定性。首先建立了随机普通不同方程与相应随机反应扩散方程之间溶液稳定性的关系。然后，通过使用Lyapunov方法，给出了足够的均方和随机稳定性的条件。结果表明，乘法噪声可以使解决方案稳定，但添加噪声不会。
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.
