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| THE DIRICHLET PROBLEM FOR DIFFUSION EQUATION |
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Citation： |
Li Zhichan,Yang Qingji.THE DIRICHLET PROBLEM FOR DIFFUSION EQUATION[J].Chinese Annals of Mathematics B,1989,10(3):301~311 |
| Page view： 881
Net amount： 825 |
Authors： |
Li Zhichan; Yang Qingji |
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| Abstract： |
Let $D$ be a bounded domain in the $d+1$-dimensional Euclidean space $\[{R^{d + 1}}\]$. This paper aims at giving a probabilistic treatment of the Dirichlet problem for the following diffusion equation on D
$$\[(1/2\Delta + q)u(x,t) = \frac{\partial }{{\partial t}}u(x,t),(x,t) \in D\]$$
where $q$ is a function to be specified later and $\[\Delta \]$ is the Laplace operator $\[\sum\limits_{i = 1}^d {\frac{{{\partial ^2}}}{{\partial x_i^2}}} \]$. The existence and uniqueness theorems are given, and furthermore, the probabilistic representation and martingale charaeteristion of the solutions for diffusion equations are obtained. |
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