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Courant Lecture Notes 2006; 217 pp; softcover Volume: 14 ISBN10: 0821835769 ISBN13: 9780821835760 List Price: US$34 Member Price: US$27.20 Order Code: CLN/14 See also: Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS  Pierpaolo Esposito, Nassif Ghoussoub and Yujin Guo  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 secondyear 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 LaxPhillips 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. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University. Readership Graduate students and research mathematicians interested in hyperbolic equations. 


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