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Titlebook: Dispersive Equations and Nonlinear Waves; Generalized Korteweg Herbert Koch,Daniel Tataru,Monica Vişan Textbook 2014 Springer Basel 2014 Fo

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发表于 2025-3-21 17:47:24 | 显示全部楼层 |阅读模式
书目名称Dispersive Equations and Nonlinear Waves
副标题Generalized Korteweg
编辑Herbert Koch,Daniel Tataru,Monica Vişan
视频video
概述Exposition of central ideas in dispersive equations.Basic techniques and function spaces.Coherent introduction to induction on energy, minimal blow up solutions and interaction Morawetz estimates.Intr
丛书名称Oberwolfach Seminars
图书封面Titlebook: Dispersive Equations and Nonlinear Waves; Generalized Korteweg Herbert Koch,Daniel Tataru,Monica Vişan Textbook 2014 Springer Basel 2014 Fo
描述The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.​
出版日期Textbook 2014
关键词Fourier transform; dispersion; wave interaction; wave propagation; partial differential equations
版次1
doihttps://doi.org/10.1007/978-3-0348-0736-4
isbn_softcover978-3-0348-0735-7
isbn_ebook978-3-0348-0736-4Series ISSN 1661-237X Series E-ISSN 2296-5041
issn_series 1661-237X
copyrightSpringer Basel 2014
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