DEPARTMENT OF MATHEMATICS
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PDE/Applied Math Seminar

Schedule for Spring 2009

Talks are  Thursdays at 3:30 pm in room 3206 MTH (the Math department colloquium room) unless noted otherwise.

If you want to receive e-mail announcements of talks please contact Antoine Mellet (mellet@math.umd.edu), or Dionisios Margetis (dio@math.umd.edu).

(Click here for previous semesters' schedules.)

January 29 NO SEMINAR
Abstract:
February 5 The interaction between nonlinear Koiter shells and viscous fluids
Arthur Cheng

CSCAMM and Department of Mathematics -- UMCP
Abstract:
February 12 An invariance principle for random traveling waves in one dimension
James Nolen
Department of Mathematics -- Duke University
Abstract: Some reaction-diffusion equations admit traveling wave solutions, which are simple models of a chemical reaction spreading with constant speed. Even in a heterogeneous medium, solutions to the initial value problem may develop an interface propagating with a well-defined asymptotic speed. I will describe an invariance principle for the random interface that develops in the solution of a reaction diffusion equation in a random medium. I will discuss the connection between this limit theorem and recent work on stability of generalized traveling waves.
February 19 RESERVED FOR THE N. WIENER CTR FOURIER TALKS
February 26

JOINT PDE/NUMERICAL ANALYSIS SEMINAR
A Singularly Perturbed Semilinear Reaction-Diffusion Problem in a Polygonal Domain
Bruce Kellogg
Mathematics and IPST, UMCP
Abstract: The semilinear reaction-diffusion equation -epsilon^2 Del^2 u + b(x,u)=0 with Dirichlet boundary conditions is considered in a convex polygonal domain. The diffusion parameter epsilon^2 is arbitrarily small, and the "reduced equation" b(x,u_0(x))=0 may have multiple solutions. An asymptotic expansion for u is constructed that involves boundary and corner layer functions. By perturbing this asymptotic expansion, we obtain certain sub- and super-solutions and thus show the existence of a solution u that is close to the constructed asymptotic expansion. The polygonal boundary forces the study of the nonlinear autonomous elliptic equation -Del^2 z+f(z)=0 posed in an infinite sector, and the well-posedness of the corresponding linearized problem. The arguments that lead to this well-posedness may have an independent interest.
The material in the talk is joint work with N. Kopteva (Limerick, Ireland).
March 5 NO SEMINAR -- CSCAMM Kinetic FRG Young Researchers Workshop

March 2-5, 2009

Abstract:
March 12 Reaction-Diffusion Equations with Nonlinear Boundary Conditions in Narrow Domains and Wave Front Propagation
Konstantinos Spiliopoulos

Department of Mathematics -- UMCP
Abstract: We will consider the second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions. Using probabilistic methods we show that the solution of such a problem converges as $\epsilon \downarrow 0$ to the solution of a standard reaction-diffusion equation in a domain of reduced dimension. This reduction allows to obtain some results concerning wave front propagation in narrow domains. In particular, we describe conditions leading to jumps of the wave front. In addition, an important and interesting problem, which is related to the previous one, is the Wiener process with instantaneous reflection in a narrow tube which, in contrast to before, is assumed to be non-smooth asymptotically.
March 19 SPRING BREAK -- NO SEMINAR
March 26 RESERVED FOR WORKSHOP
April 2 Traveling fronts in disordered media
Andrej Zlatos
Department of Mathematics -- University of Chicago
Abstract: We study generalized traveling front solutions of reaction-diffusion equations modeling flame propagation in combustible media. Although the case of periodic media has been studied extensively, until very recently little has been known for general disordered media. In this talk we will address questions of existence, uniqueness, and stability of traveling fronts in this framework.
April 9 No Seminar
Abstract:
April 16 The inviscid limit in the plane for nondecaying vorticity
Elaine Cozzi
Department of Mathematics - Carnegie Mellon University
Abstract: We consider solutions of the Navier-Stokes and Euler equations in the plane with bounded, nondecaying initial vorticity. Specifically, we assume that initial velocity has finite energy, and we show that as viscosity approaches zero, the solutions of the Navier-Stokes equations converge to the solution of the Euler equations uniformly in space, where convergence holds for any finite time. We also study the case where initial velocity is merely bounded and establish a similar short time result.
April 23
Round droplet solutions and oval droplet solutions for the Ohta-Kawasaki theory and the Gierer-Meinhardt theory
Xiaofeng Ren
Department of Mathematics -- Georges Washington University
CANCELLED
Abstract:
April 30
JOINT APPL. MATH/NUMERICAL ANALYSIS SEM.
-- AZIZ LECTURER
A New Formalism for Electromagnetic Scattering in Complex Geometry
Leslie Greengard
Courant Institute of Mathematical Sciences
New York University
Abstract: We will describe some recent, elementary results in the theory of electromagnetic scattering. There are two classical approaches that we will review - one based on the vector and scalar potential and applicable in arbitrary geometry, and one based on two scalar potentials (due to Lorenz, Debye and Mie), valid only in the exterior of a sphere. In trying to extend the Lorenz-Debye-Mie approach to arbitrary geometry, we have encountered some new mathematical questions involving differential geometry, partial differential equations and numerical analysis. This is joint work with Charlie Epstein.
May 7 OPEN
Abstract:
May 14 OPEN
Abstract:

How to reach the Math Department by car and public transportation

Special accomodations for individuals with disabilities can be made by calling in advance (301) 405-5048. It would be appreciated if we are notified at least one week in advance.

For further information contact A. Mellet at mellet@math.umd.edu, or D. Margetis at dio@math.umd.edu.