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.
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