Hyperbolic partial differential equations and geometric optics
 Author/Creator
 Rauch, Jeffrey.
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xix, 363 p. : ill ; 27 cm.
 Series
 Graduate studies in mathematics ; v. 133.
Access
Available online

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QC20.7 .S54 R38 2012

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QC20.7 .S54 R38 2012
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 351358) and index.
 Publisher's Summary
 This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations. One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader.< /p> The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics..
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Jeffrey Rauch.
 Series
 Graduate studies in mathematics ; v. 133
 ISBN
 9780821872918
 0821872915