柳田研究室

第66回東工大数理解析セミナー

2019年11月18日 (月) 17:00 -- 18:30 本館2階 213セミナー室

Bongsuk Kwon 氏(蔚山科学技術大学校)
Plasma solitary waves of the Euler-Poisson system

We discuss the existence and asymptotic behavior of plasma solitary waves of the Euler-Poisson system which arises in the dynamics of plasmas. We first show the Euler-Poisson system admits a two-parameter family of the traveling solitary wave solutions, under the super-ion-acoustic condition, and show that the solitary wave converges to that of the associated KdV equation as the traveling speed tends to the ion-acoustic speed. As solutions of the KdV equation are dominated by their solitary waves, one may expect a similar result for the Euler-Poisson system with more general data. As a first step, we investigate the linear convective stability of the solitary waves of the Euler-Poisson system. If time permits, we shall discuss some key features of the proof of the linear stability. This is joint work with J. Bae (NCTS at National Taiwan University).

次回以降の予定

2019年11月29日 (金) 17:00 -- 18:30 本館2階 213セミナー室

Chunjing Xie 氏(上海交通大学)
Uniform structural stability of Hagen-Poiseuille flows in a pipe

We discuss the recent progress on nonlinear structural stability of Hagen-Poiseuille flows, in particular, the uniform stability of these flows with respect to the mass flux. The key ingredient of the analysis is the linear structural stability of Hagen-Poiseuille flows in a pipe. This linear problem closely relates to dynamical stability of Hagen-Poiseuille flows. The existence of a class of large solutions in a pipe will also be addressed even when the external force is large.

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2019年12月4日 (水) 17:00 -- 18:30 本館2階 213セミナー室

Ulrich Menne 氏(国立台湾師範大学)
A priori diameter bounds for solutions to a variety of Plateau problems

Plateau's problem in Euclidean space may be given many distinct formulations with solutions to most of them admitting an associated varifold. This includes Reifenberg's approach based on sets and Čech homology as well as Federer and Fleming's approach using integral currents and their homology. Thus, we employ the unifying setting of varifolds to prove a priori bounds on the geodesic diameter in terms of boundary behaviour. A central challenge in this process is to determine a suitable notion of connectedness; in fact, there exist several possible definitions distinct already in the case of varifolds associated to smooth immersions. This is ongoing joint work with C. Scharrer.

http://www.math.titech.ac.jp/~yanagida/seminar.html