Hyperbolic Partial Differential Equations

Released on by Peter D. Lax
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  • Hyperbolic Partial Differential Equations Book Detail

  • Author : Peter D. Lax
  • Release Date : 2006
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 234
  • ISBN 13 : 0821835769
  • File Size : 62,62 MB
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Hyperbolic Partial Differential Equations by Peter D. Lax PDF Summary

Book 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.

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Hyperbolic Partial Differential Equations

Hyperbolic Partial Differential Equations

File Size : 63,63 MB
Total View : 7110 Views
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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, electro

Hyperbolic Partial Differential Equations

Hyperbolic Partial Differential Equations

File Size : 96,96 MB
Total View : 8012 Views
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This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is