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

点击翻译按钮获取中文摘要

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. *** ??