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. 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.
General
| Imprint: |
American Mathematical Society
|
| Country of origin: |
United States |
| Series: |
Graduate Studies in Mathematics |
| Release date: |
May 2012 |
| Authors: |
Jeffrey Rauch
|
| Dimensions: |
259 x 185 x 23mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
363 |
| ISBN-13: |
978-0-8218-7291-8 |
| Categories: |
Books
|
| LSN: |
0-8218-7291-5 |
| Barcode: |
9780821872918 |
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