Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Fall 2018-Spring 2019)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Spring 2018 | Tentative schedule for Spring 2018]]===
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===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===
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== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==
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== PDE GA Seminar Schedule Fall 2017 ==
 
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!style="width:20%" align="left" | date   
 
!style="width:20%" align="left" | date   
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!align="left" | title
 
!align="left" | title
 
!style="width:20%" align="left" | host(s)
 
!style="width:20%" align="left" | host(s)
|-
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|September 11
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|Mihaela Ifrim (UW)
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|-  
|[[#Mihaela Ifrim| Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation]]
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|September 10,
| Kim & Tran
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| Hiroyoshi Mitake (University of Tokyo)
|-
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|[[#Hiroyoshi Mitake | TBA ]]
|September 18
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|Longjie Zhang (University of Tokyo)  
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|[[#Longjie Zhang | On curvature flow with driving force starting as singular initial curve in the plane]]
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|  Angenent
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|-
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|September 22,
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VV B239 4:00pm
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|Jaeyoung Byeon (KAIST)
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|[[#Jaeyoung Byeon|  Colloquium: Patterns formation for elliptic systems with large interaction forces]]
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|  Rabinowitz
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|-
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|September 25
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| Tuoc Phan (UTK)
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|[[#Tuoc Phan |  Calderon-Zygmund regularity estimates for weak solutions of quasi-linear parabolic equations with an application. ]]
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| Tran
 
| Tran
|-  
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|-
|September 26,  
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|September 17,
VV B139 4:00pm
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| Changyou Wang (Purdue)
| Hiroyoshi Mitake (Hiroshima University)
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|[[#Changyou Wang TBA ]]
|[[#Hiroyoshi Mitake Joint Analysis/PDE seminar ]]
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| Tran
 
| Tran
 +
|- 
 +
|September 24/26,
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| Gunther Uhlmann (UWash)
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|[[#Gunther Uhlmann | TBA ]]
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| Li
 +
|- 
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|October 1,
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| Matthew Schrecker (UW)
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|[[#Matthew Schrecker | TBA ]]
 +
| Kim and Tran
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|- 
 +
|October 8,
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| Anna Mazzucato (PSU)
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|[[#Anna Mazzucato | TBA ]]
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| Li and Kim
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|- 
 +
|October 15,
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| Lei Wu (Lehigh)
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|[[#Lei Wu | TBA ]]
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| Kim
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|- 
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|October 22,
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| Annalaura Stingo (UCD)
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|[[#Annalaura Stingo | TBA ]]
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| Mihaela Ifrim
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|- 
 +
|October 29,
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| Jessica Lin (McGill University)
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|[[#Jessica Lin | TBA ]]
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| Tran
 +
|- 
 +
|November 5,
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| Albert Ai (University of Berkeley)
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|[[#Albert Ai | TBA ]]
 +
| Mihaela Ifrim
 +
|- 
 +
|December 10,
 +
|  ( )
 +
|[[#  | TBA ]]
 +
 
|-  
 
|-  
|September 29,
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|January 28,
VV901 2:25pm
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|   ( )
| Dongnam Ko (CMU & SNU)
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|[[| TBA ]]
|[[Dongnam Ko | a joint seminar with ACMS: TBD ]]
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|
| Shi Jin & Kim
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|-
|-  
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|March 4
|October 2
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| Vladimir Sverak (Minnesota)
| No seminar due to a KI-Net conference
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|[[#Vladimir Sverak | TBA(Wasow lecture) ]]
|
+
|
+
|-
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|October 9
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| Sameer Iyer (Brown University)
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|[[Sameer Iyer | TBD ]]
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| Kim
 
| Kim
|-  
+
|-
|October 16
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|March 18,
| Jingrui Cheng (UW)
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| Spring recess (Mar 16-24, 2019)
|[[Jingrui Cheng |  TBD ]]
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|[[# |  ]]
| Kim & Tran
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|   
|-  
+
|-
|October 23
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|April 29,
| Donghyun Lee (UW)
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|   ( )
|[[Donghyun Lee | TBD ]]
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|[[# | TBA ]]
| Kim & Tran
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|
|-
+
|October 30
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| Myoungjean Bae (POSTECH)
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|[[ Myoungjean Bae TBD ]]
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Feldman
+
|-  
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|November 6
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| Jingchen Hu (USTC and UW)
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|[[Jingchen Hu | TBD ]]
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| Kim & Tran
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|}
 
|}
  
==Abstracts==
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== Abstracts ==
 
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===Mihaela Ifrim===
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+
Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
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Our goal is to take a first step toward understanding the long time dynamics of solutions for the Benjamin-Ono equation. While this problem is known to be both completely integrable and globally well-posed in $L^2$, much less seems to be known concerning its long time dynamics. We present that for small localized data the solutions have (nearly) dispersive dynamics almost globally in time. An additional objective is to revisit the $L^2$ theory for the Benjamin-Ono equation and provide a simpler, self-contained approach. This is joined work with Daniel Tataru.
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===Longjie Zhang===
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On curvature flow with driving force starting as singular initial curve in the plane
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We consider a family of axisymmetric curves evolving by its mean curvature with driving force in the plane. However, the initial curve is oriented singularly at origin. We investigate this problem by level set method and give some criteria to judge whether the interface evolution is fattening or not. In the end, we can classify the solutions into three categories and provide the asymptotic behavior in each category. Our main tools in this paper are level set method and intersection number principle.
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===Jaeyoung Byeon===
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Title: Patterns formation for elliptic systems with large interaction forces
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Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions.  The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.
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+
  
===Tuoc Phan===
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=== ===
Calderon-Zygmund regularity estimates for weak solutions of quasi-linear parabolic equations with an application.
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Abstract: In this talk, we first introduce a problem on the existence of global time smooth solutions for a system of cross-diffusion equations. We then recall some classical results on regularity theories, and show that to solve our problem, new results on regularity theory estimates of Calderon-Zygmund type for gradients of solutions to a class of parabolic equations in Lebesgue spaces are required. We then discuss a result on Calderon-Zygmnud type estimate in the concrete setting to solve our
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Title:
mentioned problem regarding the system of cross-diffusion equations. The remaining part of the talk will be focused on some new generalized results on regularity gradient estimates for some general class of quasi-linear parabolic equations. Regularity estimates for gradients of solutions in Lorentz spaces will be presented. Ideas of the proofs for the results are given.
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Latest revision as of 16:35, 14 August 2018

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 2019-Spring 2020

PDE GA Seminar Schedule Fall 2018-Spring 2019

date speaker title host(s)


September 10, Hiroyoshi Mitake (University of Tokyo) TBA Tran
September 17, Changyou Wang (Purdue) TBA Tran
September 24/26, Gunther Uhlmann (UWash) TBA Li
October 1, Matthew Schrecker (UW) TBA Kim and Tran
October 8, Anna Mazzucato (PSU) TBA Li and Kim
October 15, Lei Wu (Lehigh) TBA Kim
October 22, Annalaura Stingo (UCD) TBA Mihaela Ifrim
October 29, Jessica Lin (McGill University) TBA Tran
November 5, Albert Ai (University of Berkeley) TBA Mihaela Ifrim
December 10, ( ) TBA
January 28, ( ) TBA
March 4 Vladimir Sverak (Minnesota) TBA(Wasow lecture) Kim
March 18, Spring recess (Mar 16-24, 2019)
April 29, ( ) TBA

Abstracts

Title: