Nonlinear partial differential equations (PDEs) is a vast area, and practitioners include applied mathematicians, analysts, and others in the pure and applied sciences. This introductory text on nonlinear partial differential equations evolved from a graduate course I have taught for many years at the University of Nebraska at Lincoln. It emerged as a pedagogical effort to introduce, at a fairly elementary level, nonlinear PDEs in a format and style that is accessible to students with diverse backgrounds and interests. The audience has been a mixture of graduate students from mathematics, physics, and engineering. The prerequisites include an elementary course in PDEs emphasizing Fourier series and separation of variables, and an elementary course in ordinary differential equations.
There is enough independence among the chapters to allow the instructor considerable flexibility in choosing topics for a course. The text may be used for a second course in partial differential equations, a first course in nonlinear PDEs, a course in PDEs in the biological sciences, or an advanced course in applied mathematics or mathematical modeling. The range of applications include biology, chemistry, gas dynamics, porous media, combustion, traffic flow, water waves, plug flow reactors, heat transfer, and other topics of interest in applied mathematics.
There are three major changes from the first edition, which appeared in 1994. Because the original chapter on chemically reacting fluids was highly specialized for an introductory text, it has been removed from the new edition. Additionally, because of the surge of interest in mathematical biology, considerable material on that topic has been added; this includes linear and nonlinear age structure, spatial effects, and pattern formation. Finally, the text has been reorganized with the chapters on hyperbolic equations separated from the chapters on diffusion processes, rather than intermixing them.
The references have been updated and, as in the previous edition, are selected to suit the needs of an introductory text, pointing the reader to parallel treatments and resources for further study. Finally, many new exercises have been added. The exercises are intermediate-level and are designed to build the students’ problem solving techniques beyond what is experienced in a beginning course.
1. Introduction to Partial Differential Equations
2. First-Order Equations and Characteristics
3. Weak Solutions to Hyperbolic Equations
4. Hyperbolic Systems
5. Diffusion Processes
6. Reaction-Diffusion Systems
7. Equilibrium Models
Enlaces Públicos de descarga