White noise driven quasilinear SPDEs with reflection
White noise driven quasilinear SPDEs with reflection
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DOI：
10.1007/bf01195389
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发表时间：
1992-03
影响因子：
2
通讯作者：
D. Nualart;É. Pardoux
中科院分区：
文献类型：
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作者：
D. Nualart;É. Pardoux
研究了空间区间[0，1]上的热方程在加性时空白噪声驱动下，具有Dirichlet边界条件的反射解。粗略地说，在解u(x，t)严格为正的任何点(x，t)，它服从方程，而在u(x，t)为零的点(x，t)，我们增加一个力，以防止它变为负。这可以看作是反映在0处的一维SDE的推广，也可以看作是确定性变分不等式的推广。证明了一个结果的存在唯一性，该结果在很大程度上依赖于一个确定性变分不等式的新结果。
We study reflected solutions of the heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise. Roughly speaking, at any point (x, t) where the solutionu(x, t)is strictly positive it obeys the equation, and at a point (x, t) whereu(x, t)is zero we add a force in order to prevent it from becoming negative. This can be viewed as an extension both of one-dimensional SDEs reflected at 0, and of deterministic variational inequalities. An existence and uniqueness result is proved, which relies heavily on new results for a deterministic variational inequality.