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Hyperbolic Partial Differential Equations and Geometric Optics

Jeffrey Rauch University of Michigan, Ann Arbor, MI
Available Formats:
Hardcover ISBN: 978-0-8218-7291-8
Product Code: GSM/133
363 pp
List Price: $68.00 MAA Member Price:$61.20
AMS Member Price: $54.40 Electronic ISBN: 978-0-8218-8508-6 Product Code: GSM/133.E 363 pp List Price:$64.00
MAA Member Price: $57.60 AMS Member Price:$51.20
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List Price: $102.00 MAA Member Price:$91.80
AMS Member Price: $81.60 Click above image for expanded view Hyperbolic Partial Differential Equations and Geometric Optics Jeffrey Rauch University of Michigan, Ann Arbor, MI Available Formats:  Hardcover ISBN: 978-0-8218-7291-8 Product Code: GSM/133 363 pp  List Price:$68.00 MAA Member Price: $61.20 AMS Member Price:$54.40
 Electronic ISBN: 978-0-8218-8508-6 Product Code: GSM/133.E 363 pp
 List Price: $64.00 MAA Member Price:$57.60 AMS Member Price: $51.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$102.00
MAA Member Price: $91.80 AMS Member Price:$81.60
• Book Details

Volume: 1332012
MSC: 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.

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

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• Get Permissions
Volume: 1332012
MSC: 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.

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
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