An Introduction to Nonlinear Partial Differential Equations

by J. David Logan

Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds."
―SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.

Genres: Mathematics

416 pages, Hardcover

First published April 6, 1994

Reviews

[Tomáš Ševček · Rating 5 out of 5]

An interesting read on (not only non-linear) PDEs. The book studies standard hyperbolic (waves, shock formation and propagation, discontinuities), parabolic/diffusion (traveling waves and their stability, reaction-diffusion equations, maximum principles, comparison results, energy estimates) and elliptic (stationary solutions, equilibrium models, eigenvalue problems) phenomena with plenty of applications in physics, chemistry and biology. The exposition is less formal and rigorous than in Evans, with the focus on problems and examples rather than on formal theorems and proofs. Some topics (such as bifurcations in PDEs or the many real-world examples) cannot be found in Evans (still, Evans contains most of the theoretical material covered in this book and much more). Unlike Evans, the reader does not have to be familiar with functional analysis. Some parts (such as the proof of the existence and uniqueness of the classical solution to reaction-diffusion equations) do require some basic functional analysis, but it is explained in the text, so the book is self-contained in this sense (therefore, a good grasp of calculus, ODEs and some basic PDEs will suffice). All in all, this book is excellent if you want to learn more advanced PDE techniques but do not have a solid grasp of functional analysis.