Dispersive Equations and Nonlinear Waves

Released on by Herbert Koch
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  • Dispersive Equations and Nonlinear Waves Book Detail

  • Author : Herbert Koch
  • Release Date : 2014-07-14
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 310
  • ISBN 13 : 3034807368
  • File Size : 70,70 MB
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Dispersive Equations and Nonlinear Waves by Herbert Koch PDF Summary

Book Description: 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.​

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Dispersive Equations and Nonlinear Waves

Dispersive Equations and Nonlinear Waves

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The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation an

Nonlinear Dispersive Wave Systems

Nonlinear Dispersive Wave Systems

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This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV

Linear and Nonlinear Waves

Linear and Nonlinear Waves

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Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It