M546 Introduction to Nonlinear Partial Differential Equations
Spring Semester 2005
Instructor DuChateau
M546 is a continuation of M545. It begins 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 course then begins an introduction to nonlinear partial differential equations. It surveys selected topics in nonlinear pde’s including conservation law equations, similarity solutions for nonlinear problems, traveling wave solutions.
M545 or some experience with linear PDE’s is a prerequisite.
Grades are based on problems, which are to be done outside of class and handed in from time to time. There are no in class exams.
There is no required text; instead the lectures are based on notes which are available below, together with the course syllabus.
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