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Seminar

Language	English
From	2012/06/15 15:30
To	2012/06/15 16:30
Place	Room 251, Building No.3, Faculty of Science, Kyoto University
Seminar Name	NLPDE Seminar
Title	Dispersive limit from the Kawahara to the KdV equation
Field	Analysis
Speakers	Luc Molinet
Affiliation	Universite Francois-Rabelais de Tours
Abstract	We will discuss the limit behavior of the solutions to the Kawahara equation $u_t + u_{3x} + \varepsilon u_{5x} + u u_x = 0, \varepsilon>0$ as $\varepsilon \to 0$ . In this equation, the terms $u_{3x}$ and $\varepsilon u_{5x}$ do compete together and do cancel each other at frequencies of order $1/\sqrt{\varepsilon}$ . This prohibits the use of a standard dispersive approach for this problem. Nevertheless, by combining different dispersive approaches according to the range of spaces frequencies, we will see that the solutions to this equation converge in $C([0,T];H^1(R))$ towards the solutions of the KdV equation for any fixed $T>0$ .
Link	http://www.math.kyoto-u.ac.jp/~n-kishi/nlpde/