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 auchmuty@uh.edu.
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