Math 295abc - Partial Differential
Equations
Class is scheduled for
MWF 1:00-1:50 in
MSTB 114
Partial Differential Equations are a multifaceted subject with several
and deep connections to other areas of mathematics, such as differential
geometry, functional analysis, mathematical physics, applied mathematics,
harmonic analysis, ...
It should therefore not come as a surprise that a wide range of methods and
techniques have been developed for their treatment. This course is intended
to be an introduction and an overview highlighting the diverse aspects of
PDEs which make up its nevertheless organic body.
I. Term
(September 2001 - December 2001)
-
Introduction and Motivation.
-
The theory of Distributions.
-
Fundamental Solutions.
-
Sobolev Spaces and Trace Theorems.
-
Weak Solvability Theory of Uniformly
Elliptic Boundary Value Problems.
-
Linear Evolution Equations I.
Assignments in DVI and PDF format:
Homework 1 (dvi, pdf)
Homework 2 (dvi, pdf)
Homework 3 (dvi, pdf)
Homework 4 (dvi, pdf)
Homework 5 (dvi, pdf)
II. Term
(January 2002 - March 2002)
-
Semigroup Theory.
-
Linear Evolution Equations II.
-
Conservation Laws and Hamilton Jacobi equations.
Assignments in DVI and PDF format:
Homework 1 (dvi, pdf)
Homework 2 (dvi, pdf)
Homework 3 (dvi, pdf)
Homework 4 (dvi, pdf)
III. Term
(April 2002 - June 2002)
-
Fixed-Point Theorems.
-
Maximum Principles.
-
Galerkin Method.
-
Variational Methods.
Assignments in DVI and PDF format:
Homework 1 (dvi, pdf)
Homework 2 (dvi, pdf)
Suggested Literature
- L. C. Evans, Partial Differential
Equations , Graduate Studies in Mathematics Vol. 19, AMS 1998.
- M. E. Taylor, Partial Differential
Equations, Volumes 1 and 3, Springer 1996.
- M. F. John, Partial Differential
Equations, Springer IV Ed 1982.
- D. Mitrovic, D. Zubrinic, Fundamentals
of Applied Functional Analysis , Pitman Monographs and Surveys in Pure
and Applied Mathematics, Longman 1998.
- K. Yosida, Functional Analysis,
Springer 1980.
- A. Pazy, Semigroups of Linear Operators
and Applications to Partial Differential Equations, Springer 1983.
- R. Dautray, J. L. Lions, Mathematical
Analysis and Numerical Methods for Science and Technology, Vol. II,
Springer 1990.
- J. L. Lions, E. Magenes, Non-Homogeneous
Boundary Value Problems and Applications I, II, III, Springer 1972/73.
- R. A. Adams, Sobolev Spaces,
Academic Perss 1975.