If you want to receive e-mail announcements of talks please contact
Manoussos Grillakis (mng@math.umd.edu)
or Dionisios Margetis (dio@math.umd.edu).
| September 14
|
Regularizing effects in hyperbolic, parabolic and elliptic nonlinear PDEs
Eitan Tadmor,
Department of Mathematics, CSCAMM and IPST -- UMCP
|
|
Abstract: Velocity averaging is used to study the regularizing effects in
quasilinear second-order equations, L(D_x,u)u=S(u) using their underlying
kinetic formulations, L(D_x,v)\chi(u,v)=g_S(v). Our study of velocity
averaging
applies to a large class of operators satisfying the so-called truncation
multiplier property, which is shown to include all L's of degree\leq 2. In
particular, we improve previous regularity statements for multidimensional
conservation laws, and we derive completely new regularity results for
related
convection-diffusion and elliptic equations driven by degenerate,
non-isotropic
diffusion.
|
| September 21
|
Existence results for some nonlinear hyperbolic equations on a
waveguide
Ann Stewart,
Department of Mathematics -- UMCP
|
|
Abstract: We will present existence theorems for nonlinear wave and
Klein-Gordon equations with small initial data and quadratic
nonlinearities in infinite homogeneous waveguides. We are able to
show that solutions exist globally on waveguides with certain
Robin boundary conditions and almost globally with Neumann
boundary conditions.
|
| September 28
|
NO SEMINAR
|
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Abstract:
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| October 5
|
On kinetic models for dilute
suspensions of rigid rods
Athanasios Tzavaras, Department of Mathematics -- UMCP
|
|
Abstract:
We discuss the existence theory for certain kinetic models
modeling
dilute suspensions of rigid rods. The model consists of a Smoluchowski
equation
describing the evolution of a micro-scale coupled with Stokes flow for the
motion
of the solvent. For certain parameter values, the stress vs. velocity
gradient curve
for a stationary and homogeneous flow is not rank-one monotone. This allows
for steady states that exhibit discontinuities in velocity gradient,
associated
to shear bands. For the dynamic problem, we consider the evolution of
possibly
large perturbations of stationary flows and prove that, even in the absence
of a microscopic
cut-off, jump discontinuities cannot occur in finite time.
|
| October 12
|
Estimates for eigenfunctions of the Laplacian
Christopher Sogge,
Department of Mathematics --
Johns Hopkins
|
|
Abstract:
I shall present various L^p estimates for eigenfunctions
of the Laplacian in manifolds with and without boundary. A common
theme
is to try to see how the underlying geometry, as measured by the
long-term dynamics of the geodesic flow, does or does not lead to
blowup of
L^p norms. In the case where $p=\infty$ we shall also discuss
blowup and non-blowup results for quasimodes.
|
| October 19
|
Joint Math/CSCAMM/Norbert-Wiener-Center Seminar:
Fast Algorithms for Sparse Analysis
Anna Gilbert, Department of Mathematics -- University of Michigan
|
|
Abstract:
I will present several extremely fast algorithms for recovering a
compressible signal from a few linear measurements. These examples
span a variety of orthonormal bases, including one large redundant
dictionary. As part of the presentation of these algorithms, I will
give an explanation of the crucial role of group testing in each
algorithm.
|
| October 26
|
Searching for Singularities in Incompressible Flow
Russel Caflisch, Department of Mathematics --
University of California, Los Angeles
|
|
Abstract:
For the last 50 years, the possibility of singularity formation has been an
open problem for the Euler equations of incompressible, inviscid fluid flow.
Onszager was the first to conjecture
singularity formation as a mechanism for inviscid energy dissipation.
Subsequent analytic and
numerical studies have illuminated a number of possibilities and limitations
for singularity formation, but so far there is no convincing evidence for or
against Onsager's conjecture. This talk will describe the status of the
search for Euler singularities, in particular the role of complex
singularities.
|
| November 2
|
Constant mean curvature graphs in MxR
Joel Spruck, Department of Mathematics -- Johns Hopkins
|
|
Abstract:
We study cmc graphs in the product space MxR where M is an arbitrary
n dimensional Riemannian manifold. We emphasize a pde point of view
and an important element of our discussion of the Dirichlet problem
are interior gradient estimates and height estimates. As an application,
we will indicate (as time permits) the extension of the results of my 1971
thesis
on infinite boundary value problems in R^3 (after Jenkin-Serrin for H=0)
to H^2xR and S^2xR.
|
| November 9
|
Numerical
simulation of
acoustic
streaming on surface acoustic wave-
driven
biochips
Daniel Koester, Institute of Mathematics -- University of Augsburg
|
|
Abstract:
A novel type of microfluidic biochip employs surface acoustic waves
as a contact-free pumping mechanism for fluids. The interaction
of these waves with an adjoining fluid volume leads to streaming
patterns in the fluid, or of the motion of the fluid as a whole.
In this work we study this acoustic streaming effect. We present a
mathematical model, some theoretical results on the well-posedness of
the model problem, as well as numerical simulations based on the
Finite Element Method. The model will include the case of free
capillary fluid boundaries.
|
| November 16
|
Stability of rotating star solutions for compressible Euler-Poisson
equations
Tao Luo, Department of Mathematics --
Georgetown University
|
|
Abstract:
In this talk, I will present some results of stability of rotating star
solutions for compressible Euler-Poisson equations. The rotating
star solutions discussed here are the minimizers of an energy functional
with prescribed angular momentum and total mass. This is joint work
with Joel Smoller.
|
| November 23
|
Thanksgiving Holiday - No Seminar
|
|
|
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November 30
|
Optimal illumination in array imaging
George Papanicolaou, Department of Mathematics -- Stanford University
|
|
Abstract:
I will discuss the mathematical problem of optimally illuminating an object
for imaging by an array. In a certain regime of parameters and for a special
class of objects this can be done by using spheroidal wave functions. In
general situations one must use algorithms that optimally image the object
by detecting its edges. Such algorithms are very different from the ones
that maximize the energy of the signals received by the array so as to
enhance detectability. I will analyze and compare the two types of
algorithms. (Joint work with L. Borcea and C. Tsogka.)
|
| December 7
|
Recent progress on the L^{2}-critical, defocusing semilinear
Schrödinger equation
Nikolaos Tzirakis, Department of Mathematics -- University of Toronto
|
|
Abstract:
In this talk I will describe the progress that has been made so far
concerning the existence of global strong solutions to the L^{2}-critical
defocusing semilinear Schrödinger equation. A long standing conjecture in the
area is the existence of a unique global strong L^{2} solution to the
equation that in addition scatters to a free solution as time goes to
infinity. I will demonstrate the proofs of partial results towards
an attempt for a final resolution of this conjecture. I will
concentrate on the low dimensions but give the flavor of the
results in higher dimensions for general or spherically symmetric
initial data in certain Sobolev spaces. Many authors have contributed
to the theory of this equation. I will convey my personal involvement
to the problem and the results that I have obtained recently.
Part of my work is in collaboration with D. De Silva, N. Pavlovic,
G. Staffilani, J. Colliander and M. Grillakis.
|
| December 14
|
Regularity and analyticity for the quasi-geostrophic equations
and the Navier-Stokes equations
Hongjie Dong, School of Mathematics --
Institute for Advanced Study, Princeton
|
|
Abstract:
This talk is devoted to higher order regularity and analyticity
rate estimates for the dissipative quasi-geostrophic equations
and the Navier-Stokes equations with possible fractional
dissipation.
Some decay in time estimates will also be discussed. It is
based on joint work with D. Du and recent joint work with D.
Li.
|
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.
