Introduction to Nonlinear Partial Differential Equations

These notes were used in a brief introduction to nonlinear partial differential equations. We begin, however, with a brief treatment of existence/uniqueness results for weak solutions to elliptic boundary value problems using Hilbert space techniques. This material provides a theoretical basis for finite element method for computing weak solutions.

The notes then begin an introduction to nonlinear partial differential equations. We survey selected topics in nonlinear pde’s including conservation law equations, similarity solutions for nonlinear problems, traveling wave solutions.

Introduction to the Method of Characteristics

Problems on Systems of Conservation Laws

Travelling Wave Solutions to NL PDE's

Existence, Uniqueness and Asymptotic Behavior

There is no single text, which covers all of the material that is listed above. Some texts, which cover various parts of the material and are available in low cost Dover versions are the following:

**Partial Differential Equations
of Mathematical Physics** by Guenther and Lee

**Applied Partial Differential
Equations** by DuChateau and Zachmann

**A First Course in Partial
Differential Equations** by Weinberger

**Introduction to Partial
Differential Equations** by Zachmonoglou and Thoe

**Equations of Mathematical Physics** by
Tikhonov and Samarskii

**Introduction
to Partial Differential Equations and Hilbert Space Methods** by Karl
Gustafson