Biography: Itaru Hataue is a professor of Kanazawa University, Japan. He received a Ph. D in engineering from the University of Tokyo in 1989, a master degree in engineering in 1984 and a bachelor degree in engineering in 1982 at Kyoto University. From 1987 to 1990, he was an assistant professor at the University of Tokyo. From 1990 to 1992, he was an assistant professor at Kyoto University. He was a lecturer from 1992 to 1994 and an associate professor from 1994 to 2003 at Kumamoto University. From 2003, he has been a professor at Kanazawa University. His research interests include numerical simulation for nonlinear phenomena, dependence of numerical solutions on randomness and improvement of the reliability of simulated results.
Speech Title: Dependence of numerical solutions of nonlinear PDE on forcibly added randomness
Abstract: Random effects for the numerical solutions of compressible Navier-Stokes equations and reaction-diffusion equations are discussed in this work. In the first research, we considered the cases that random noises are forcibly added to physical quantities of the transonic flow around an elliptic cylinder. Obtained results show that disturbance induced by added noises at coarse grid system in the windward region strongly affects the flow structure around the elliptic cylinder. In the second research, the dependence of asymptotic solutions of one- and two-dimensional reaction–diffusion system with the FitzHugh–Nagumo model on added random noises was studied. When several kinds of asymptotic solutions coexist in a parameter region, the nearly equal stability of those solutions induce the appearance of the locally connecting bistable solutions (LCBSs). Dependence of structure of the dynamical LCBSs on random noises was clarified.