| SoftcoverISBN: | 978-0-8218-3576-0 |
| Product Code: | CLN/14 |
| List Price: | $39.00 |
| MAA Member Price: | $35.10 |
| AMS Member Price: | $31.20 |
| eBookISBN: | 978-1-4704-3114-3 |
| Product Code: | CLN/14.E |
| List Price: | $36.00 |
| MAA Member Price: | $32.40 |
| AMS Member Price: | $28.80 |
| SoftcoverISBN: | 978-0-8218-3576-0 |
| eBookISBN: | 978-1-4704-3114-3 |
| Product Code: | CLN/14.B |
| List Price: | $75.00$57.00 |
| MAA Member Price: | $67.50$51.30 |
| AMS Member Price: | $60.00$45.60 |
| Softcover ISBN: | 978-0-8218-3576-0 |
| Product Code: | CLN/14 |
| List Price: | $39.00 |
| MAA Member Price: | $35.10 |
| AMS Member Price: | $31.20 |
| eBook ISBN: | 978-1-4704-3114-3 |
| Product Code: | CLN/14.E |
| List Price: | $36.00 |
| MAA Member Price: | $32.40 |
| AMS Member Price: | $28.80 |
| Softcover ISBN: | 978-0-8218-3576-0 |
| eBookISBN: | 978-1-4704-3114-3 |
| Product Code: | CLN/14.B |
| List Price: | $75.00$57.00 |
| MAA Member Price: | $67.50$51.30 |
| AMS Member Price: | $60.00$45.60 |
-
Book DetailsCourant Lecture NotesVolume: 14; 2006; 217 ppMSC: Primary 35;Peter D. Lax is the winner of the 2005 Abel Prize
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject.
The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves.
The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today.
Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses.
Peter D. Lax is the winner of the 2005 Abel Prize. Read more here.ReadershipGraduate students and research mathematicians interested in hyperbolic equations.
-
Table of Contents
-
Chapters
-
Chapter 1. Basic notions
-
Chapter 2. Finite speed of propagation of signals
-
Chapter 3. Hyperbolic equations with constant coefficients
-
Chapter 4. Hyperbolic equations with variable coefficients
-
Chapter 5. Pseudodifferential operators and energy inequalities
-
Chapter 6. Existence of solutions
-
Chapter 7. Waves and rays
-
Chapter 8. Finite difference approximation to hyperbolic equations
-
Chapter 9. Scattering theory
-
Chapter 10. Hyperbolic systems of conservation laws
-
Appendix A. Huygens’ principle for the wave equation on odd-dimensional spheres
-
Appendix B. Hyperbolic polynomials
-
Appendix C. The multiplicity of eigenvalues
-
Appendix D. Mixed initial and boundary value problems
-
Appendix E. Energy decay for star-shaped obstacles
-
-
Additional Material
-
RequestsReview Copy – for reviewers who would like to review an AMS bookAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject.
The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves.
The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today.
Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses.
Peter D. Lax is the winner of the 2005 Abel Prize. Read more here.
Graduate students and research mathematicians interested in hyperbolic equations.
-
Chapters
-
Chapter 1. Basic notions
-
Chapter 2. Finite speed of propagation of signals
-
Chapter 3. Hyperbolic equations with constant coefficients
-
Chapter 4. Hyperbolic equations with variable coefficients
-
Chapter 5. Pseudodifferential operators and energy inequalities
-
Chapter 6. Existence of solutions
-
Chapter 7. Waves and rays
-
Chapter 8. Finite difference approximation to hyperbolic equations
-
Chapter 9. Scattering theory
-
Chapter 10. Hyperbolic systems of conservation laws
-
Appendix A. Huygens’ principle for the wave equation on odd-dimensional spheres
-
Appendix B. Hyperbolic polynomials
-
Appendix C. The multiplicity of eigenvalues
-
Appendix D. Mixed initial and boundary value problems
-
Appendix E. Energy decay for star-shaped obstacles
