Talks Titles and Abstracts
Hotels in Manhattan
KSU Math Department
Previous Prairie Seminars
Location and Dates:
Department of Mathematics
Kansas State University
November 2-3, 2007
University of Texas at Austin
Title: Fully non linear
equations with integral diffusions
Abstract: Fully non linear
equations arise in optimal control (Hamilton Jacobi equations) when we
are allowed to choose in each step the best diffusion to fit our
purpose, and in Game Theory (Isaac 's equation) when competing players
alternatively choose their most convenient diffusion.
There is a
rather complete theory in the case in which the underlying diffusions
are continuous (Wiener processes).
describe recent work (with L. Silvestre) where a parallel theory is
develop for discontinuous (Levy) processes.
is available at arXiv.org
University of British Columbia
Title: Hele-Shaw flows
and obstacle problems: Application to random homogenization.
Abstract: It is a well-known fact
that Hele-Shaw and Stefan free boundary problems can be formally
formulated as obstacle problems via an integration in time. Using the
notion of viscosity solutions, we make this connection more rigorous.
We then deduce some results on the periodic and random homogenization
of Hele-Shaw type free boundary problems, when oscillations arise along
the free boundary.
Title: Modeling and
stability for bent-core liquid crystal molecules
investigate a model for drawn fibers made up of cylindrical, smectic
layers of banana-shaped liquid crystal molecules. The molecular shape
induces both a spontaneous polarization and a distinctive effect on
layer density. These features lead to a model that predicts stable
fiber formation. We cast the model as a free boundary problem for the
fiber's cross-section and
analyze its solutions. This is
joint work with P.Bauman.
There will be time allocated for short contributed talks by
participants. Priority will be given to graduate students and those
in early stages of their carriers.
Participants interested in given a contributed talk and/or receiving
financial support should visit the
Estela A. Gavosto, KU
Marianne Korten, KSU
Diego Maldonado, KSU
Charles Moore, KSU
Virginia Naibo, KSU
Rodolfo H. Torres, KU