Designed to bridge the gap between graduate-level
texts in partial differential equations and the
current literature in research journals, this text
introduces students to a wide variety of more
modern methods -- especially the use of functional
analysis -- which has characterized much of the
recent development of PDEs.
covers the modern, functional
analytic methods in use today -- especially as
they pertain to nonlinear equations.
maintains mathematical rigor and
generality whenever possible -- but not at the
expense of clarity or concreteness.
offers a rapid pace -- with some
proofs and applications relegated to exercises.
unlike other texts -- which start with
the treatment of second-order equations --
begins with the method of characteristics and
first-order equations, with an emphasis in its
introduces the methods by emphasizing
features important applications
from physics and differential geometry -- e.g.,
Navier-Stokes, Klein-Gordon, Prescribed Scalar and
illustrates topics with many figures.
contains nearly 400 exercises,
most with hints or solutions.
locates exercises near relevant
provides chapter summaries.
lists references for further
1. First-Order Equations.
2. Principles for Higher-Order Equations.
3. The Wave Equation.
4. The Laplace Equation.
5. The Heat Equation.
6. Linear Functional Analysis.
7. Differential Calculus Methods.
8. Linear Elliptic Theory.
9. Two Additional Methods.
10. Systems of Conservation Laws.
11. Linear and Nonlinear Diffusion.
12. Linear and Nonlinear Waves.
13. Nonlinear Elliptic Equations.
Hints and Solutions of Selected