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