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= PDE and Geometric Analysis Seminar - Fall 2010=
+
The seminar will be held  in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
  
The seminar will be held  in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
+
===[[Previous PDE/GA seminars]]===
 +
===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
== Seminar Schedule ==
 
{| cellpadding="8"
 
!align="left" | date 
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | host(s)
 
|-
 
|Sept 13
 
|Fausto Ferrari (Bologna)
 
|[[#Fausto Ferrari (Bologna)|
 
''Semilinear PDEs and some symmetry properties of stable solutions'']]
 
|Misha
 
|-
 
|Sept 27
 
|Arshak Petrosyan (Purdue)
 
|[[#Arshak Petrosyan (Purdue)|
 
''Nonuniqueness in a free boundary problem from combustion'']]
 
|Misha
 
|-
 
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck.  '''Special day, time & room.'''
 
|Changyou Wang (U. of Kentucky)
 
|[[#Changyou Wang (U. of Kentucky)|
 
''Phase transition for higher dimensional wells'']]
 
|Misha
 
|-
 
|Oct 11
 
|Philippe LeFloch (Paris VI)
 
|[[#Philippe LeFloch (Paris VI)|
 
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]
 
|Misha
 
|-
 
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck.    '''Special day, time & room.'''
 
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)
 
|[[#Irina Mitrea |
 
''Boundary Value Problems for Higher Order Differential Operators'']]
 
|[https://www.math.wisc.edu/~wimaw/ WiMaW]
 
|-
 
|-
 
|Nov 1
 
|Panagiota Daskalopoulos (Columbia U)
 
|[[#Panagiota Daskalopoulos (Columbia U)|
 
''Ancient solutions to geometric flows'']]
 
|Misha
 
|-
 
|Nov 8
 
|Maria Gualdani (UT Austin)
 
|[[#Maria Gualdani (UT Austin)|
 
''A nonlinear diffusion model in mean-field games'']]
 
|Misha
 
|-
 
|Date TBA
 
|Mikhail Feldman (UW Madison)
 
|''TBA''
 
|Local speaker
 
|-
 
|Date TBA
 
|Sigurd Angenent (UW Madison)
 
|''TBA''
 
|Local speaker
 
|-
 
|}
 
== Abstracts ==
 
===Fausto Ferrari (Bologna)===
 
''Semilinear PDEs and some symmetry properties of stable solutions''
 
  
I will deal with stable solutions of semilinear elliptic PDE's
 
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.
 
  
===Arshak Petrosyan (Purdue)===
+
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==
''Nonuniqueness in a free boundary problem from combustion''
+
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. 
 +
 
 +
'''Week 1 (9/1/2020-9/5/2020)'''
 +
 
 +
1. Paul Rabinowitz - The calculus of variations and phase transition problems.
 +

https://www.youtube.com/watch?v=vs3rd8RPosA
 +
 
 +
2. Frank Merle - On the implosion of a three dimensional compressible fluid.
 +
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 
 +
 
 +
'''Week 2 (9/6/2020-9/12/2020)'''
 +
 
 +
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.
 +
https://www.youtube.com/watch?v=4ndtUh38AU0
 +
 
 +
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI
 +
 
 +
 
 +
 
 +
'''Week 3 (9/13/2020-9/19/2020)'''
 +
 
 +
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ
 +
 
 +
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE
 +
 
 +
 
 +
 
 +
'''Week 4 (9/20/2020-9/26/2020)'''
 +
 
 +
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be
 +
 
 +
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM
 +
 
 +
 
 +
 
 +
'''Week 5 (9/27/2020-10/03/2020)'''
 +
 
 +
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo
 +
 
 +
2.  Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c
 +
 
 +
 
 +
'''Week 6 (10/04/2020-10/10/2020)'''
 +
 
 +
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E
 +
 
 +
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing
 +
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html
 +
 
 +
 
 +
'''Week 7 (10/11/2020-10/17/2020)'''
 +
 
 +
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s
 +
 
 +
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg
 +
 
 +
 
 +
'''Week 8 (10/18/2020-10/24/2020)'''
 +
 
 +
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg
 +
 
 +
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ
 +
 
 +
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.
 +
 
 +
 
 +
'''Week 9 (10/25/2020-10/31/2020)'''
 +
 
 +
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE
 +
 
 +
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764
 +
 
 +
 
 +
 
 +
'''Week 10 (11/1/2020-11/7/2020)'''
 +
 
 +
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be
 +
 
 +
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html
 +
 
 +
 
 +
 
 +
'''Week 11 (11/8/2020-11/14/2020)'''
 +
 
 +
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc
 +
 
 +
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0
 +
 
 +
 
 +
'''Week 12 (11/15/2020-11/21/2020)'''
 +
 
 +
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY
 +
 
 +
2.  Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk
 +
 
 +
 
 +
'''Week 13 (11/22/2020-11/28/2020)'''
 +
 
 +
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be
 +
 
 +
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8
 +
 
 +
'''Week 14 (11/29/2020-12/5/2020)'''
 +
 
 +
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations,
 +
https://youtu.be/xfAKGc0IEUw
 +
 
 +
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc
 +
 
 +
 
 +
 
 +
'''Week 15 (12/6/2020-12/12/2020)'''
 +
 
 +
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be
 +
 
 +
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU
  
We consider a parabolic free boundary problem with a fixed gradient condition
 
which serves as a simplified model for the propagation of premixed equidiffusional
 
flames. We give a rigorous justification of an example due to J.L. V ́azquez that
 
the initial data in the form of two circular humps leads to the nonuniqueness of limit
 
solutions if the supports of the humps touch at the time of their maximal expansion.
 
  
This is a joint work with Aaron Yip.
+
'''Spring 2021'''
  
 +
'''Week  ( / /2021- / /2021)'''
  
===Changyou Wang (U. of Kentucky)===
+
1. Emmanuel Grenier -  instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be
''Phase transition for higher dimensional wells''
 
  
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected
+
2.
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:
 
  
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.
 
  
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as  the parameter <math>\epsilon</math>
+
'''Week ( / /2021- / /2021)'''
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and
 
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary
 
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.
 
  
===Philippe LeFloch (Paris VI)===
+
1. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''
 
  
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physicsIn the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves.
+
2.   
  
  
 +
'''Week  ( / /2021- / /2021)'''
  
===Irina Mitrea===
+
1. Hao Jia -  nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg
''Boundary Value Problems for Higher Order Differential Operators''
 
  
As is well known, many phenomena in engineering and mathematical physics
+
2.
can be modeled by means of boundary value problems for a certain elliptic
 
differential operator L in a domain D.
 
  
When L is a differential operator of second order a variety of tools
 
are available for dealing with such problems including boundary integral
 
methods,
 
variational methods, harmonic measure techniques, and methods based on
 
classical
 
harmonic analysis. The situation when the differential operator has higher order
 
(as is the case for instance with anisotropic plate bending when one
 
deals with
 
fourth order) stands in sharp contrast with this as only fewer options
 
could be
 
successfully implemented. Alberto Calderon, one of the founders of the
 
modern theory
 
of Singular Integral Operators, has advocated in the seventies the use
 
of layer potentials
 
for the treatment of higher order elliptic boundary value problems.
 
While the
 
layer potential method has proved to be tremendously successful in the
 
treatment
 
of second order problems, this approach is insufficiently developed to deal
 
with the intricacies of the theory of higher order operators. In fact,
 
it is largely
 
absent from the literature dealing with such problems.
 
  
In this talk I will discuss recent progress in developing a multiple
 
layer potential
 
approach for the treatment of boundary value problems associated with
 
higher order elliptic differential operators. This is done in a very
 
general class
 
of domains which is in the nature of best possible from the point of
 
view of
 
geometric measure theory.
 
  
 +
{| cellpadding="8"
 +
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|- 
 +
|}
  
===Panagiota Daskalopoulos (Columbia U)===
+
== Abstracts ==
''Ancient solutions to geometric flows''
 
  
We will discuss the clasification of ancient solutions to nonlinear geometric flows.
+
=== ===
It is well known that ancient solutions appear as blow up limits  at a finite time 
 
singularity of the  flow.
 
Special emphasis will be given to the 2-dimensional Ricci flow.
 
In this case we will show that ancient  compact solution
 
is either the Einstein (trivial)  or one of the King-Rosenau solutions.
 
  
===Maria Gualdani (UT Austin)===
+
Title: 
''A nonlinear diffusion model in mean-field games''
 
  
We present an overview of mean-field games theory and show
+
Abstract:
recent results on a free boundary value problem, which models
 
price formation dynamics.
 
In such model, the price is formed through a game among infinite number
 
of agents.
 
Existence and regularity results, as well as linear stability, will be shown.
 

Latest revision as of 08:06, 12 January 2021

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Previous PDE/GA seminars

Tentative schedule for Fall 2021-Spring 2022

PDE GA Seminar Schedule Fall 2020-Spring 2021

Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. 

Week 1 (9/1/2020-9/5/2020)

1. Paul Rabinowitz - The calculus of variations and phase transition problems. 
https://www.youtube.com/watch?v=vs3rd8RPosA

2. Frank Merle - On the implosion of a three dimensional compressible fluid. https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 

Week 2 (9/6/2020-9/12/2020)

1. Yoshikazu Giga - On large time behavior of growth by birth and spread. https://www.youtube.com/watch?v=4ndtUh38AU0

2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI


Week 3 (9/13/2020-9/19/2020)

1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ

2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE


Week 4 (9/20/2020-9/26/2020)

1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be

2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM


Week 5 (9/27/2020-10/03/2020)

1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo

2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c


Week 6 (10/04/2020-10/10/2020)

1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E

2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html


Week 7 (10/11/2020-10/17/2020)

1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s

2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg


Week 8 (10/18/2020-10/24/2020)

1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg

2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ

Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.


Week 9 (10/25/2020-10/31/2020)

1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE

2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764


Week 10 (11/1/2020-11/7/2020)

1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be

2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html


Week 11 (11/8/2020-11/14/2020)

1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc

2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0


Week 12 (11/15/2020-11/21/2020)

1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY

2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk


Week 13 (11/22/2020-11/28/2020)

1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be

2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8

Week 14 (11/29/2020-12/5/2020)

1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, https://youtu.be/xfAKGc0IEUw

2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc


Week 15 (12/6/2020-12/12/2020)

1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be

2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU


Spring 2021

Week ( / /2021- / /2021)

1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be

2.


Week ( / /2021- / /2021)

1. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE

2.


Week ( / /2021- / /2021)

1. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg

2.


date speaker title host(s)

Abstracts

Title:

Abstract: