Ohio State University Partial Differential Equations Seminar
Year 2019-2020
Time/Location: Tuesdays 1:50pm- 2:50pm / MW154 (unless otherwise noted) |
Schedule of talks:
|
| TIME |
SPEAKER |
TITLE |
HOST |
August 27
| No seminar
() |
|
|
September 3
| No seminar
() |
|
|
September 10
| No seminar
() |
|
|
September 17
| No seminar
() |
|
|
September 19
Joint with DG
CH240, 3:00-4:00pm
| Yannick Sire
(Johns Hopkins) |
Half-harmonic maps, minimal surfaces with free boundary and Ginzburg-Landau approximation |
Guan |
September 24
| Juhi Jang
(USC) |
Newtonian gravitational collapse beyond dust dynamics |
Xing |
October 1
| No seminar
() |
|
|
October 8
| No seminar
() |
|
|
October 15
| No seminar
() |
|
|
October 22
| No seminar
() |
|
|
October 29
| No seminar
() |
|
|
November 5
| No seminar
() |
|
|
November 12
Joint with DG
| Nam Le
(Indiana) |
The Brunn-Minkowski inequality for the Monge-Ampere eigenvalue and smoothness of the eigenfunctions |
Guan |
November 19
| No seminar
() |
|
|
November 26
| No seminar
() |
|
|
December 3
Joint with Probability
| Alex Hening
(Tufts) |
Stochastic persistence and extinction |
Lou |
December 5
Joint with DG
| Qing Han
(Notre Dame) |
The Loewner-Nirenberg Problem in Cones |
Guan |
December 10
| No seminar
() |
|
|
December 17
| No seminar
() |
|
|
December 24
| No seminar
() |
|
|
January 7
|
No Seminar
() |
|
|
January 14
|
No Seminar
() |
|
|
January 21
|
No Seminar
() |
|
|
January 28
|
No Seminar
() |
|
|
February 4
|
No Seminar
() |
|
|
February 11
CH240
Special Date 11am-noon |
No Seminar
() |
|
|
February 18
|
No Seminar
() |
|
|
February 25
|
No Seminar
() |
|
|
March 3
|
Adrian Lam
(OSU) |
Recent results in Evolution of Dispersal |
|
March 10
|
No Seminar
() |
|
|
March 17
|
Benoit Perthame
(Sorbonne Univ.) |
Aronson-Benilan estimate and incompressible limit in tumor growth models |
Lam/Lou |
March 24
| No seminar
() |
|
|
March 31
|
Emeric Bouin
(Dauphine) |
|
Lou |
April 7
Joint with Applied Math |
Ivan Sudakov
(Dayton) |
|
Lam |
April 14
|
No Seminar
() |
|
|
April 21
|
Connor Mooney
(UC Irvine) |
|
Guan |
April 28
|
No seminar
() |
|
|
Abstracts
Yannick Sire, Johns Hopkins (Sep 19, 2019) Joint with differential geometry
Title: Half-harmonic maps, minimal surfaces with free boundary and Ginzburg-Landau approximation
Abstract: I will report on results related to a new program giving a new viewpoint on an old topic, minimal surfaces with free boundary. I will describe first the standard theory of harmonic maps before moving to the case of half-harmonic maps (into spheres) introduced by Da Lio and Riviere. The main part of the talk will be to describe the Ginzburg-Landau approximation of those latter maps. I will describe several open problems and possible new directions of research.
Juhi Jang, Univ. South California (Sep 24, 2019)
Title: Newtonian gravitational collapse beyond dust dynamics
Abstract: The classical model of an isolated self-gravitation gaseous star is the Euler-Poisson system with a polytropic pressure law. For any adiabatic exponent between 1 and 4/3, we construct an infinite-dimensional family of collapsing solutions to the Euler-Poisson system whose density is in general space inhomogeneous and undergoes gravitational blowup along a prescribed space-time surface, with continuous mass absorption at the origin. The leading order singular behavior is described by an explicit collapsing solution of the pressureless Euler-Poisson system.
Nam Le, Indiana (Nov 12, 2019)
Title: The Brunn-Minkowski inequality for the Monge-Ampere eigenvalue and smoothness of the eigenfunctions
Abstract: The original form of the Brunn-Minkowski inequality involves volumes of convex bodies in R^n and states that the n th root of the volume is a concave function with respect to the Minkowski addition of convex bodies. In 1976, Brascamp and Lieb proved a Brunn-Minkowski inequality for the first eigenvalue of the Laplacian. In this talk, I will discuss a nonlinear analogue of the above result, that is, the Brunn-Minkowski inequality for the eigenvalue of the Monge-Ampere operator. For this purpose, I will first introduce the Monge-Ampere eigenvalue problem on general bounded convex domains. Then, I will present several properties of the eigenvalues and related analysis concerning smoothness of the eigenfunctions.
Alex Hening, Tufts (Dec 3, 2019)
Title: Stochastic persistence and extinction
Abstract: A key question in population biology is understanding the conditions under which the species of an ecosystem persist or go extinct. Theoretical and empirical studies have shown that persistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n interacting species that live in a stochastic environment. Our models are described by n dimensional piecewise deterministic Markov processes. These are processes (X(t), r(t)) where the vector X denotes the density of the n species and r(t) is a finite state space process which keeps track of the environment. In any fixed environment the process follows the flow given by a system of ordinary differential equations. The randomness comes from the changes or switches in the environment, which happen at random times. We give sharp conditions under which the populations persist as well as conditions under which some populations go extinct exponentially fast. As an example we show how the random switching can `rescue' species from extinction.
Qing Han, Notre Dame (Dec 5, 2019)
Title: The Loewner-Nirenberg Problem in Cones
Abstract: Loewner and Nirenberg discussed complete metrics conformal to the Euclidean metric and with a constant scalar curvature in bounded domains in the Euclidean space. The conformal factors blow up on boundary. The asymptotic behaviors of the conformal factors near boundary are known in C^2-domains. In this talk, we discussasymptotic behaviors near vertices of cones.
Adrian Lam, OSU (Mar 3, 2020)
Title: Recent results in Evolution of Dispersal
Abstract: In this talk, we will talk about some recent PDE
results in evolution of dispersal. First, we will discuss the
progress on two-species competition in an advective environment
and its subtle dependence on boundary conditions and domain size.
Next, we will discuss moving Dirac solutions in a nonlocal PDE
proposed by Perthame and Souganidis. This latter equation
describes a population structured by space and a phenotypic
trait, and can be understood as competition of infinitely many
species.
Benoit Perthame, Univ. Sorbonne (Mar 17, 2020)
Title: Aronson-Benilan estimate and incompressible limit in tumor growth models
Abstract: Models of tissue growth are now well established, in particular, in relation to their
applications to cancer. They describe the dynamics of cells subject to motion resulting from a
pressure gradient generated by the death and birth of cells, itself controlled primarily by
pressure through contact inhibition. In the compressible regime, pressure results from the cell
densities and when two different populations of cells are considered, a specific difficulty arises;
the equation for each cell density carries a hyperbolic character, and the equation for the total
cell density has a degenerate parabolic property. For that reason, few a priori estimates are
available and discontinuities may occur. Therefore the existence of solutions is a difficult problem.
Here, we establish the existence of weak solutions to the model with two cell populations which react
similarly to the pressure in terms of their motion but undergo different growth/death rates. In opposition
to the method used in the recent paper of Carrillo et al., our strategy is to ignore compactness of
the cell densities and to prove strong compactness of the pressure gradient. For that, we propose a
new version of Aronson–Bénilan estimate, working in L^2 rather than L^\infinity. We improve known results in three
directions; we obtain new estimates, we treat dimensions higher than 1 and we deal with singularities
resulting from vacuum.
Emeric Bouin, Dauphine (Mar 31, 2020)
Title: TBD
Abstract: TBD
Ivan Sudakov, University of Dayton (Apr 7, 2020)
Title: TBD
Abstract: TBD
Connor Mooney, UC Irvine (Apr 21, 2020)
Title: TBD
Abstract: TBD
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