| 随机一般多孔介质与快速扩散方程 |
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| 引用本文： | 王凤雨. 随机一般多孔介质与快速扩散方程[J]. 山东大学学报(理学版), 2009, 44(10): 1-13 |
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| 作者姓名： | 王凤雨 |
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| 作者单位： | 北京师范大学数学科学学院数学与系统科学实验室; |
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| 基金项目： | Supported in part by NNSFC(10721091) and the 973-Project |
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| 摘 要： | 基于作者和合作者的有关工作,本文介绍关于随机一般多孔介质与快速扩散方程研 究的若干新进展。我们从确定性的方程出发，引入相应随机方程的一般框架，再分别介绍解的存在唯一性、Harnack 不等式与应用、解的正则性和大偏差原理等。
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| 关 键 词： | 随机多孔介质方程；随机快速扩散方程；Harnack不等式；大偏差；遍历 |
| 收稿时间： | 2007-07-16 |
On stochastic generalized porous media and fast diffusion equations |
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| Feng-Yu Wang. On stochastic generalized porous media and fast diffusion equations[J]. Journal of Shandong University, 2009, 44(10): 1-13 |
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| Authors: | Feng-Yu Wang |
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| Affiliation: | School of Mathematical Sci. and Lab. Math. Com. Sys., Beijing Normal University, Beijing 100875, China and Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, UK |
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| Abstract: | In terms of some recent work of the author and collaborators,this paper provides a self-contained account for the study of stochastic generalized porous media and fast-diffusion equations.We start from the corresponding deterministic equations in PDEs to explain the framework of the study,then introduce,respectively,results on the existence and uniqueness of solutions,the Harnack inequality for the associated transition semigroups and applications,the L2-solutions and Large deviation principles with small n... |
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| Keywords: | stochastic porous media equations stochastic fast diffusion equations Harnack inequality large deviations ergodicity |
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