慶應義塾大学 理工学部 数理科学科

非線形解析セミナー

タイトル On the Favrie-Gavrilyuk approximation to the Serre-Green-Naghdi system
開催日時 2019年6月28日 16:45-18:15
主催者
講演者 Professor Vincent Duchene(University of Rennes)
場所 慶應義塾大学理工学部 14棟 631B
(創想館 6階 ミーティング1B)
内容 The Serre-Green-Naghdi system (SGN) is a fully nonlinear and weakly dispersive model for the propagation of surface gravity waves. Recently, N. Favrie and S. Gavrilyuk proposed a strategy for producing approximate solutions with the aim of removing numerical difficulties due to the presence of high-order differential operators in SGN. They introduced an "augmented" first-order quasilinear system of balance laws depending on additional unknows and a free parameter. The claim is that in the singular limit when the parameter goes to infinity, solutions of the augmented system approach solutions of SGN. We will discuss a rigorous analysis, based on pioneering works of G. Browning and G.-O. Kreiss, and S. Schochet in the 80's. However, we will see that the presence of order-zero source terms in the singular system of Favrie and Gavrilyuk, as well as the coexistence of two singular parameters (hence three time scales) demand substantial adjustments to the strategy of the aforementioned works.
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