The Fields Institute Colloquium/Seminar in Applied Mathematics
is a monthly colloquium series intended to be a focal point for
mathematicians in the areas of applied mathematics and analysis.
The series consists of talks by internationally recognized experts
in the field, some of whom reside in the region and others who are
invited to visit especially for the colloquium.

In recent years, there have been numerous dramatic successes in
mathematics and its applications to diverse areas of science and
technology; examples include super-conductivity, nonlinear wave
propagation, optical fiber communications, and financial modeling.
The intent of the Colloquium series is to bring together the applied
mathematics community on a regular basis, to present current results
in the field, and to strengthen the potential for communication
and collaboration between researchers with common interests. We
meet for one session per month during the academic year.

**PAST SEMINARS July 1, 2004-June
30, 2005**

**June 7, 2005**

**Y. S. Choi**, University of Connecticut

*Moving Boundary Problem for a One-dimensional Crawling Nematode
Sperm Cell Model*

The movement of cells along surfaces is fundamental to many
important biological processes such as embryogenesis and functioning
of the cellular immune system. A promising one dimensional cell
motility model has been proposed by Mogilner and Verzi in 2003.
It consists of a system of coupled parabolic and hyperbolic
equations with moving boundaries representing the front and
the back ends of the cell. Under some assumptions on the parameters
and the initial data in the model, we prove the global existence
of the solution. We also establish the existence and uniqueness
of traveling wave to the model. Numerical experiments suggest
that such traveling wave solution may be globally asymptotically
stable.

**May 11, 2005**

**Ralph Saxton**, University of New Orleans and Fields Institute

*Boundary layer separation and breakdown*

We examine unsteady solutions to the Prandtl system, a simplification
of the Navier-Stokes equations used to describe the motion of
fluids having small viscosity, in the thin layer which forms
in a neighbourhood of a solid body due to friction. Our aim
is to show that an adverse pressure gradient can lead to this
layer separating, which is a precursor to the eventual breakdown
of solutions.

**March 30, 2005 **

**Katarina Jegdic**, University of Houston and Fields Institute

*Transonic regular reflection for the unsteady transonic small
disturbance equation*

We study a Riemann problem for the unsteady transonic small
disturbance equation resulting in a regular reflection with
the subsonic state behind the reflected shock. We formulate
the problem using the self-similar coordinates and obtain a
free boundary value problem which exhibits the change of type.
A solution is found in a neighborhood of the reflection point
using the fixed point theory and Schauder estimates for the
mixed boundary value problems.

**February 23, 2005**- 3:10 p.m. Room 230

**Allen Tesdall**, University of Houston and Fields Institute

*Self-similar and steady solutions for weak shock reflection*

We describe numerical methods for computing solutions of
the unsteady transonic small disturbance equations that describe
the Mach reflection of weak shock waves. We solve the equations
in self-similar variables and use local grid refinement to resolve
the solution in the reflection region. The solutions contain
a complex structure consisting of a sequence of triple points
and tiny supersonic patches directly behind the leading triple
point, formed by the reflection of weak shock and expansion
waves between the sonic line and the Mach shock. The presence
of an expansion fan at each triple point resolves the von Neumann
triple point paradox. Additionally, we will present some self-similar
solutions for the reflection of expansion waves.

**February 16, 2005** -- Seminar in Applied Mathematics

**Katarzyna Saxton,** Department of Mathematics, Loyola
University, New Orleans

*Low Temperature Phase Transitions in Heat Propagation.*

**November 4 , 2004** -- 2:10-3:00 Colloquium in Applied Mathematics

**Charles Fefferman**, Princeton University

*Whitney's Extension Problem II*

**October 20, 2004** -- 3:10 p.m. Seminar in Applied Mathematics

**Nedyu Popivanov**

University of Karlsruhe, Germany and University of Sofia, Bulgaria

*50 Years Nonclassical Protter Problems
for the Wave Equation*

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