<p>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. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.</p>

Hyperbolic Partial Differential Equations (Courant Lecture Notes in Mathematics)

Science & Math

PETER D. LAX

Mathematics

American Mathematical Society/Courant Institute of Mathematical Sciences

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Books by American Mathematical Society/Courant Institute of Mathematical Sciences

See the best price to sell, buy or rent books by the American Mathematical Society/Courant Institute of Mathematical Sciences publisher. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Hyperbolic Partial Differential Equations (Courant Lecture Notes in Mathematics)