Partial Differential Equations: Methods and Applications

For a one-year, graduate-level course in Partial Differential Equations.

Designed to bridge the gap between introductory texts in partial differential equations and the current literature in research journals, this text introduces students to the basics of classical PDEs and to a wide variety of more modern methods―especially the use of functional analysis―which has characterized much of the recent development of PDEs. Throughout, the results are almost completely self-contained.

Designed to prepare readers to better understand the current literature in research journals, this book explains the basics of classical PDEs and a wide variety of more modern methods—especially the use of functional analysis—which has characterized much of the recent development of PDEs. It gives equal treatment to elliptic, hyperbolic, and parabolic theory, and features an abundance of applications to equations that are important in physics and engineering—both on the basic and more advanced level. Provides worked, figures and illustrations, and extensive references to other literature. First-Order Equations. Principles for Higher-Order Equations. The Wave Equation. The Laplace Equation. The Heat Equation. Linear Functional Analysis. Differential Calculus Methods. Linear Elliptic Theory. Two Additional Methods. Systems of Conservation Laws. Linear and Nonlinear Diffusion. Linear and Nonlinear Waves. Nonlinear Elliptic Equations. Appendix on Physics. For anyone using PDEs in physics and engineering applications.