SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions
SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions
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DOI：
10.1080/1045112031000080833
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发表时间：
2003-06
期刊：
影响因子：
--
通讯作者：
Tusheng Zhang;Weian Zheng
中科院分区：
文献类型：
--
作者：
Tusheng Zhang;Weian Zheng
本文考虑高维时空白色噪声驱动的随机偏微分方程。我们证明，在合理的条件下，该法律的解决方案承认一个密度关于勒贝格措施。当高阶微分算子趋于零时，本文还研究了方程的稳定性。
In this paper, we consider stochastic partial differential equations driven by space-time white noise in high dimensions. We prove, under reasonable conditions, that the law of the solution admits a density with respect to Lebesgue measure. The stability of the equation, as the higher order differential operator tends to zero, is also studied in the paper.