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.





Intro to Hilbert Space

            Hilbert-Space Problems


Weak Solutions of BV Probs



Introduction to the Method of Characteristics 


Conservation Law Eqs I    

Conservation Law Eqs II         

Problems on Shocks and Fans


Conservation Law Eqs III

Systems pt I

Systems pt II

Problems on Systems of Conservation Laws

Travelling Wave Solutions to NL PDE's

Exact Solutions for NL PDE's

Problems on Travelling Waves

Reaction Diffusion Equations

Reaction Diffusion Eqs ptII

Similarity Solutions

Existence, Uniqueness and Asymptotic Behavior

Final Problems



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