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Hyperbolic partial differential equations

Author: Peter D Lax
Publisher: New York : Courant Institute of Mathematical Sciences ; Providence, R.I. : American Mathematical Society, ©2006.
Series: Courant lecture notes in mathematics, 14.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
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:  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Peter D Lax
ISBN: 9780821835760 0821835769
OCLC Number: 70867119
Description: vii, 217 p. : ill. ; 26 cm.
Contents: Basic notions --
Finite speed of propagation of signals --
Hyperbolic equations with constant coefficients --
Hyperbolic equations with variable coefficients --
Pseudodifferential operators and energy inequalities references --
Existence of solutions --
Waves and rays --
Finite difference approximation to hyperbolic equations --
Scattering theory --
Hyperbolic systems of conservation laws --
Huygens' principle for the wave equation on odd-dimentsinal spheres --
Hyperbolic polynomials --
Multiplicity of eigenvalues --
Mixed initial and boundary value problems --
Energy decay for star-shaped obstacles.
Series Title: Courant lecture notes in mathematics, 14.
Responsibility: Peter D. Lax ; with an appendix by Cathleen S. Morawetz.
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Abstract:

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  Read more...

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schema:description"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. -- Back cover."@en
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