Math 6327   Partial Differential Equations, Spring 2018.

The class  will be held  Tu-Th 4-5.15pm in AH15. Office hours are Tu-Th 2.30-3.30pm in PGH696  or by appointment.

This class is largely independent of Math 6326 but assumes a knowledge of Lebesgue measure, weak differential calculus and some linear analysis including the theory of continuous linear maps between Hilbert spaces as was used in M6326.

 Also a good knowledge of classical multivariable  calculus and some theory of bilinear forms.

This semester the course will treat some basic issues in the analysis of linear evolution equations. The emphasis will be on the construction of weak solutions of evolution equations using Galerkin and spectral methods. These are general approaches  that enable results about linear parabolic equations (the heat or diffusion equation), and some linear hyperbolic equations such as the wave equation. They are the methods that underlie many computational  approaches to approximating solutions.

There is no prescribed text for the course and the instructor will provide  notes for some of the material. Some of the material is covered in

Ralph E. Showalter, "Hilbert Space Methods in Partial Differential Equations" 
The treatment will be quite different to that of this text. The text is available free on the internet or from Dover Publications.

 E. Zeidler, "Nonlinear Functional Analysis and its Applications", vol IIA, Springer.

L.C. Evans, "Partial Differential Equations", AMS, chapter 7.

A well known text on numerical analysis of these problems is V. Thomee, "Galerkin Finite Element Mathods for Parabolic problems",2nd ed Springer.  The course will
describe some of the theory behind the numerical methods described in the text.

Some homework will be assigned usually background material for topics covered in class.  There will not be any exams for the course.

If you have any questions, please call me at 713-743-3475 or  e-mail to



Current Address: Department of Mathematics, PGH Building, University of Houston, Houston, Texas 77204-3008
Phone(UH): (713) 743-3500 - Fax(UH): (713) 743-3505