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

INT-9704231 Woyczynski 这项美国-波兰合作研究的主题是“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 Wojbor Woyczynski 博士和波兰弗罗茨瓦夫数学研究所的 Piotr Biler 博士。 他们提出了对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线和抛物椭圆模型的随机和非随机问题的研究。 尽管物理学界和工程学界最近提出并大力研究了此类模型，但并没有像主要研究人员提出的那样对该主题进行系统、严格的数学研究。 该研究将包括研究具有随机数据和/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全局解中的作用以及爆炸时间附近的后向自相似方程。 特别是，分形伯格斯方程和弗拉索夫-泊松-玻尔兹曼系统的随机问题将引起人们的兴趣。 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，在共同感兴趣和能力强的领域结合互补的努力和能力。 *** ??

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. *** ??