我們考慮隨機熱傳導方程，即熱傳導方程加一擾動項，在我們的前一項工作裡，我們證明了解收斂到零。我們希望能夠找到收斂的速度。另外我們也考慮隨機的Allen-Cahn方程式，對於擾動小的噪聲，希望能證明有兩個不同的不變測度。 ;We consider stochastic heat equation, namely a heat equation with a random noise. In our previous work, we have shown that the solution goes to zero. In this project we aim to find the convergence rate. Also we consider stochastic Allen-Cahn equation. We suspect that if the noise level is low, then there exist two invariant measures.
