Dispersive Equations and Nonlinear Waves: Generalized by Herbert Koch,Daniel Tataru,Monica Vişan PDF

By Herbert Koch,Daniel Tataru,Monica Vişan

ISBN-10: 303480735X

ISBN-13: 9783034807357

the 1st a part of the ebook offers an advent to key instruments and methods in dispersive equations: Strichartz estimates, bilinear estimates, modulation and tailored functionality areas, with an program to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, international options to the defocusing challenge, and scattering are the focal point of the second one half. utilizing this concrete instance, it walks the reader throughout the induction on strength method, which has turn into the basic technique for tackling huge facts severe difficulties. This contains refined/inverse Strichartz estimates, the lifestyles and nearly periodicity of minimum blow up options, and the advance of long-time Strichartz inequalities. The 3rd half describes wave and Schrödinger maps. beginning through development heuristics approximately multilinear estimates, it offers an in depth define of this very energetic quarter of geometric/dispersive PDE. It specializes in innovations and concepts and may offer graduate scholars with a stepping stone to this fascinating path of research.

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Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps (Oberwolfach Seminars) by Herbert Koch,Daniel Tataru,Monica Vişan


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