Hyperbolic Equations with Random Boundary Conditions
Hyperbolic Equations with Random Boundary Conditions
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具有随机边界条件的双曲方程
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
S. Peszat
中科院分区：
文献类型：
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作者：
Z. Brzeźniak;S. Peszat
通过适当地选择空间U，从A的预解集ρ（A）中选取一个算子E ∈ L（U，H）和一个标量λ.本文将u定义为U-值càdlàg过程的时间导数。我们将讨论问题（0.1.1）解的存在性和正则性。这个抽象的框架将由波动方程和输运方程来说明。让我们简单地描述一下本文所研究的问题的历史。据我们（非常有限）的知识，第一篇论文，研究演化问题的边界噪声是一个文件Balakrishnan。该论文研究的方程在时间上是一阶的，在空间上是四阶的，带有Dirichlet边界噪声。后来Sowers研究了一般的Neumann型反应扩散方程
by choosing properly the space U , an operator E ∈ L(U ,H) and a scalar λ from the resolvent set ρ(A) of A. In this paper u will the time derivative of a U-valued càdlàg process ξ. We will discuss the existence and regularity of a solution to the problem (0.1.1). The abstract framework will be illustrated by the wave and the transport equations. Let us describe briefly the history of the problem studied in this paper. To our (very limited) knowledge, the first paper which studied evolution problems with boundary noise was a paper by Balakrishnan. The equation studied in that paper was first order in time and fourth order in space with Dirichlet boundary noise. Later Sowers investigated general reaction diffusion equation with Neumann type