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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Hyperbolic Partial Differential Equations (Paperback, Illustrated Ed)
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Hyperbolic Partial Differential Equations (Paperback, Illustrated Ed)
Series: Courant Lecture Notes
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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. Information for our distributors: Titles in this series are
copublished with the Courant Institute of Mathematical Sciences at
New York University.
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