Nonlinear Partial Differential Equations for Scientists and Engineers

by Lokenath Debnath

"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." - Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership.

Genres: Mathematics

593 pages, Hardcover

First published August 19, 1997

Reviews

[Tomáš Ševček · Rating 5 out of 5]

A very informative textbook on (primarily non-linear) PDEs. The book covers a wide range of topics such as variational principles, characteristics, conservation laws, shock waves, dispersive waves, reaction-diffusion equations, solitons, inverse scattering transform, asymptotic methods and others (many of which cannot be found either in such a detail or altogether in Evans). While the topics are advanced, the exposition is quite simple (considering how advanced the topics are) and definitely less formal/rigorous than in Evans, with the focus on the analysis of concrete PDEs/problems rather than on general theorems and proofs. Not much functional analysis is required (not even in the parts on variational principles; real analysis/basic concepts from functional analysis will generally suffice). I recommend the book to anyone who is interested in advanced PDE techniques and their direct applications to a vast range of (natural) real-world phenomena.