zbMATH — the first resource for mathematics

Wave propagation and time reversal in randomly layered media. (English) Zbl 1386.74001
Stochastic Modelling and Applied Probability 56. New York, NY: Springer (ISBN 978-0-387-30890-6/hbk). xx, 612 p. (2007).
Publisher’s description: Wave propagation in random media is an interdisciplinary field that has emerged from the need in physics and engineering to model and analyze wave energy transport in complex environments.
This book gives a systematic and self-contained presentation of wave propagation in randomly layered media using the asymptotic theory of ordinary differential equations with random coefficients.
The first half of the book gives a detailed treatment of wave reflection and transmission in one-dimensional random media, after introducing gradually the tools from partial differential equations and probability theory that are needed for the analysis. The second half of the book presents wave propagation in three-dimensional randomly layered media along with several applications, primarily involving time reversal. Many new results are presented here for the first time.
The book is addressed to students and researchers in applied mathematics that are interested in understanding how tools from stochastic analysis can be used to study some intriguing phenomena in wave propagation in random media. Parts of the book can be used for courses in which random media and related homogenization, averaging, and diffusion approximation methods are involved.

74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
74J30 Nonlinear waves in solid mechanics
35R60 PDEs with randomness, stochastic partial differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
74E35 Random structure in solid mechanics
76Q05 Hydro- and aero-acoustics
78A48 Composite media; random media in optics and electromagnetic theory
94A05 Communication theory