权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

U.S.-Polish Collaborative Research: Fractal Models of Hydrodynamic Type

美波合作研究：流体动力型分形模型

基本信息

批准号：
9704231
负责人：
Wojbor Woyczynski
金额：
$ 3.17万
依托单位：
Case Western Reserve University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1997
资助国家：
美国
起止时间：
1997-07-15 至 2000-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704231&HistoricalAwards=false
关键词：
U.S.Polish Collaborative Research Fractal

项目摘要

INT-9704231 Woyczynski This U.S.-Poland Collaborative Research is on "Fractal Models of Hydrodynamic Type." The principal investigators are Dr. Wojbor Woyczynski of Case Western Reserve University and Dr. Piotr Biler of the Mathematical Institute of Wroclaw, Poland. They propose a study of random and nonrandom problems for nonlocal nonlinear parabolic and parabolic-elliptic models of the hydrodynamic type with fractal anomalous diffusive behavior. While the physics and engineering communities have recently suggested and vigorously studied such models, there is no systematic, rigorous mathematical study of the subject, such as the principal investigators propose. The research will include an investigation of the asymptotics of solutions with random data and/or stochastic perturbations, stochastic stability of attractors, the role of the forward self-similar solutions in description of global solutions and the backward self-similar equations near the blow-up time. In particular, random problems for the fractal Burgers equation and Vlasov-Poisson-Boltzmann systems will be of interest. This research in mathematics fulfills the program objectives of bringing together leading experts in the U.S. and Poland to combine complementary efforts and capabilities in areas of strong mutual interest and competence on the basis of equality, reciprocity, and mutuality of benefit. *** ??

INT-9704231 Woyczynski 这个美国-波兰的合作研究项目是“流体动力学类型的分形模型。“主要研究人员是凯斯西储大学的Wojbor Woyczynski博士和波兰弗罗茨瓦夫数学研究所的Piotr Biller博士。他们提出研究具有分形异常扩散行为的流体动力学类型的非局部非线性抛物和抛物椭圆模型的随机和非随机问题。虽然物理和工程界最近提出并大力研究了这些模型，但还没有像主要研究人员所建议的那样，对这个问题进行系统的、严格的数学研究。研究内容包括随机数据和/或随机扰动下解的渐近性、吸引子的随机稳定性、前向自相似解在描述全局解中的作用以及爆破时刻附近的后向自相似方程。特别是，分形Burgers方程和Vlasov-Poisson-Boltzmann系统的随机问题将感兴趣。这项数学研究实现了汇集美国和波兰领先专家的计划目标，在平等，互惠和互利的基础上，在强烈的共同利益和能力领域联合收割机互补努力和能力。 *** ??