Hardcover ISBN:  9780821872918 
Product Code:  GSM/133 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $54.40 
Electronic ISBN:  9780821885086 
Product Code:  GSM/133.E 
List Price:  $64.00 
MAA Member Price:  $57.60 
AMS Member Price:  $51.20 

Book DetailsGraduate Studies in MathematicsVolume: 133; 2012; 363 ppMSC: Primary 35; 78; 93;
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 carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations.
One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader.
The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.ReadershipGraduate students and research mathematicians interested in partial differential equations.

Table of Contents

Chapters

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


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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 carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations.
One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader.
The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.
Graduate students and research mathematicians interested in partial differential equations.

Chapters

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