Description

Book Synopsis
This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics presented are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves.

Table of Contents
  • Preface
  • Chapter 1. Simple examples of propagation
  • Chapter 2. The linear Cauchy problem
  • Chapter 3. Dispersive behavior
  • Chapter 4. Linear elliptic geometric optics
  • Chapter 5. Linear hyperbolic geometric optics
  • Chapter 6. The nonlinear Cauchy problem
  • Chapter 7. One phase nonlinear geometric optics
  • Chapter 8. Stability for one phase nonlinear geometric optics
  • Chapter 9. Resonant interaction and quasilinear systems
  • Chapter 10. Examples of resonance in one dimensional space
  • Chapter 11. Dense oscillations for the compressible Euler equations
  • Bibliography
  • Index

Hyperbolic Partial Differential Equations and

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    A Hardback by Jeffrey Rauch

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 5/30/2012 12:00:00 AM
      ISBN13: 9780821872918, 978-0821872918
      ISBN10: 0821872915

      Description

      Book Synopsis
      This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics presented are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves.

      Table of Contents
      • Preface
      • Chapter 1. Simple examples of propagation
      • Chapter 2. The linear Cauchy problem
      • Chapter 3. Dispersive behavior
      • Chapter 4. Linear elliptic geometric optics
      • Chapter 5. Linear hyperbolic geometric optics
      • Chapter 6. The nonlinear Cauchy problem
      • Chapter 7. One phase nonlinear geometric optics
      • Chapter 8. Stability for one phase nonlinear geometric optics
      • Chapter 9. Resonant interaction and quasilinear systems
      • Chapter 10. Examples of resonance in one dimensional space
      • Chapter 11. Dense oscillations for the compressible Euler equations
      • Bibliography
      • Index

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