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Giles Auchmuty
Professor
of Mathematics
- University
of Houston
Office
Location:
PGH 696
Telephone:
(713) 743-3475
Fax:
(713) 743-3505
E-mail:
auchmuty@uh.edu
My
physical, and
mail, addresses
are
University of
Houston
Department of
Mathematics
PGH Rm 696
4800 Calhoun Ave,
Houston, TX
77204-30 |
Teaching:
In
Spring
2012,
I will
teach Math
6327 Partial
Differential Equations.
For
more information
about the
courses and a
listing of courses
taught in recent
years please
select the
Teaching
link above.
Research Interests:
My
research centers on
the mathematical
analysis of problems
that arise in physical
or engineering
applications.
Currently my primary
interest is in
the solution of
div-curl systems
which arise in both
electromagnetic field
theory and in fluid
mechanics. Also
various non-standard
eigenvalue problems
and questions of how
to describe the
dependence of the
solutions of partial
differential equations
on non-trivial
boundary data. The
mathematical basis of
these theory centers
on issues about
Sobolev spaces and
associated trace
spaces. Recently I
developed a spectral
theory of trace spaces
and have obtained new
trace inequalities.
Also I have published
papers on traces for
mixed boundary
problems and for
interface and immersed
boundary
problems. This
analysis
involves the theory of
Steklov and other
eigenproblems and
Reproducing Kernel
Hilbert spaces.
Another
continuing research
interest is in the
theory of potentials
for various classes of
3-dimensional vector
fields when various
types of boundary
conditions are
imposed. Recently I
have found extensions
of the Sobolev
imbedding theorems for
3-d fields where
integrability
conditions are imposed
on the Laplacian of a
potential - but not on
the function itself.
This is the
physical
situation for
gravitational and
electrostatic
potentials. Together
with Qi Han, we are
studying the
represntation of
functions and fields
in exterior regions in
space.
This
research
is currently supported
by NSF award DMS
1108754 to study
"Steklov spectra and
Div-curl
analysis".
Maxwell's equations
are the most important
examples of div-curl
systems. See the link
to Research for more
information.
The work on these
issues is theoretical
mathematics, involving
functional analysis
and variational
principles. It
does not involve
computational
studies and I do
not have positions
available for
programmers.
Research Students:
A
list of former Ph.D.
Students
who have graduated.
Currently I am
advising Qi Han, Manki
Cho and Liu Puchen on
their doctoral
research.
I have also supervised
many M.S. theses and
some undergraduate
honors students and
other research
projects. I will
be happy to talk to
students who are
interested in possible
research projects and
know some mathematical
analysis.
Editorial:
This
section associated
with SIAM Review
welcomes unsolved
problems in applied
and applicable
mathematics.
Contributors should
send proposed problems
to Cecil C Rousseau.
If you can solve
posted problems please
let the proposer and
SIAM know about your
solutions.
Houston
Journal of
Mathematics.
The
Houston Journal of
Mathematics publishes
original research
results in many areas
of mathematics. See
their web-page Houston
J. of Mathematics
for details of the
submission process.
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