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

INT-9704231 WOYCZINSKI这项美国-波兰合作研究项目是关于“流体动力类型的分形模型”。主要研究人员是凯斯西储大学的沃伊博尔·沃伊琴斯基博士和波兰弗罗茨瓦夫数学研究所的皮奥特·比勒博士。他们研究了具有分形反常扩散行为的流体力学类型的非局部非线性抛物型和抛物型椭圆型模型的随机和非随机问题。虽然物理界和工程界最近提出了这样的模型，并对其进行了积极的研究，但还没有像主要研究人员所提出的那样，对这个主题进行系统的、严格的数学研究。研究内容包括：具有随机数据和/或随机扰动的解的渐近性、吸引子的随机稳定性、前向自相似解在描述整体解中的作用以及在爆破时间附近的后向自相似方程。特别是，关于分数维Burgers方程和Vlasov-Poisson-Boltzmann系统的随机问题将是人们感兴趣的。这项数学研究实现了将美国和波兰的顶尖专家聚集在一起，在平等、互惠和互利的基础上，在共同利益和能力强的领域结合互补努力和能力的计划目标。*？？

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. *** ??