Stochastic Partial Differential Equations with Two Reflecting Walls
Stochastic Partial Differential Equations with Two Reflecting Walls
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发表时间：
2006-10
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通讯作者：
Y. Otobe
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作者：
Y. Otobe
研究了具有两个反射光滑壁h1和h2的时空白色噪声驱动的随机偏微分方程。如果解保持在开区间（h1（x，t），h2（x，t）），则动力学服从通常类型的SPDE，并且在解的值为h1或h2的点处，我们施加力以防止它离开区间（h1，h2）。我们将首先证明解的存在性和唯一性，然后研究动力学的平稳分布和相应的Dirichlet形式。
We study stochastic partial differential equations (SPDEs) driven by space-time white noise with two reflecting smooth walls h1 and h2. If the solution stays in the open interval (h1(x, t), h2(x, t)), the dynamics obeys a usual type of SPDEs, and at a point where the value of the solution is h1 or h2, we add forces in order to prevent it fromexiting the interval ( h1 ,h 2). We will first show the existence and uniqueness of the solutions, and secondly study the stationary distribution of the dynamics and corresponding Dirichlet forms.