An Introduction to Nonlinear Partial Differential Equations

This introductory textbook on nonlinear partial differential equations is technique oriented with an emphasis on applications and is designed to build a foundation for studying advanced treatises in the field. The Second Edition features an updated bibliography as well as an increase in the number of exercises. All software references have been updated with the latest version of MATLAB, the the corresponding graphics have also been updated using MATLAB. An increased focus on hydrogeology and mathematical biology is evident in the new edition. Hints and solutions to selected exercises have been added to the back of the book. The book emphasizes hyperbolic and parabolic problems and includes a range of applications in the following areas: biology, chemistry, porous media, biological problems, combustion and detonation, traffic flow, water waves, plug flow reactors, and heat transfer. Early chapters offer insight into how to understand problems involving phenomena, how specific equations describe evolutionary processes, and what the terms in such equations describe physically. When discussing wave propagination and hyperbolic problems, the text develops algorithms to solve first-order equations and highlights the concept of the weak solution. The material in the book is presented in such a manner that many of the chapters are independent, which allows for instructors flexibility to design several courses around various topics.