Asymptotic problems for stochastic partial differential equations
Asymptotic problems for stochastic partial differential equations
批准号:
1407615
负责人:
Sandra Cerrai
金额:
$32.1万
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
2014
资助国家:
美国
项目状态:
已结题
起止时间:
2014-07-01 至 2019-06-30
中文摘要
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英文摘要
The objective of this research project is the development of new methods for the analysis of systems described by partial differential equations, in the presence of a noisy (random) perturbation and small parameters. We are interested in the description of the different behaviors of such systems, when the parameters are vanishing, and of the interplay between different limiting regimes. In particular, we will study new mathematical problems which are important for applications, as well as new effects in classical problems. The treatment of these problems for systems with an infinite number of degrees of freedom is a relatively new field of investigation, which has already stirred up a vivid interest in many fields, also because these are very complex objects and any effort that goes in the direction of their simplification is important for a deeper understanding of the main features of the models and for a better effectiveness in applications. Our analysis requires the development of new methods and the substantial introduction of new techniques which have to range over many fields in mathematics. Our goal in this proposal is studying small deterministic and stochastic perturbations of a wide class of systems described by stochastic partial differential equations. As a matter of fact, small perturbations, which are negligible on one time scale, can become crucial on a larger time scale. The long-time influence of small perturbations has been considered in a number of our previous papers, and the present project has to be considered as a continuation of this program. Limit theorems, especially the large deviation theory, the averaging principle and the interplay between them, as well as several generalizations of the Smoluchowskii-Kramers approximation are our main tools. Systems with many/infinite degrees of freedom often have perturbations of different origin and different order. Long-time behavior of such perturbed systems should be described by a hierarchy of approximations. On the other hand, long-time behavior of pure deterministic systems with instabilities, under certain conditions, should be described by a stochastic process. Therefore, the natural generality for the problem is in considering both deterministic and stochastic perturbations of stochastic systems (not necessarily deterministic dynamical systems).
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会议论文
Multiscale Analysis of Infinite-Dimensional Stochastic Systems
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批准号:1954299
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项目类别:Standard Grant
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资助金额:$30.0万
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财政年份:2020
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负责人:Sandra Cerrai
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依托单位:
Analysis of stochastic partial differential equations with multiple scales
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批准号:1712934
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项目类别:Continuing Grant
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资助金额:$36.0万
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财政年份:2017
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负责人:Sandra Cerrai
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依托单位:
Seminar on Stochastic Processes 2016
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批准号:1550644
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项目类别:Standard Grant
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资助金额:$4.77万
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财政年份:2016
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负责人:Sandra Cerrai
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依托单位:
Asymptotic problems for stochastic partial differential equations
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批准号:0907295
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项目类别:Standard Grant
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资助金额:$25.5万
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财政年份:2009
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负责人:Sandra Cerrai
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依托单位:
国内基金
海外基金
复杂图像处理中的自由非连续问题及其水平集方法研究
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批准号:60872130
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项目类别:面上项目
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资助金额:28.0万元
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批准年份:2008
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负责人:刘国才
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依托单位: