Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Fall 2017)
(Abstracts)
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==Abstracts==
 
==Abstracts==
  
===Mihaela Ifrim (UW)===
+
===Mihaela Ifrim===
  
 
Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
 
Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation

Revision as of 13:08, 7 September 2017

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 Spring 2018

PDE GA Seminar Schedule Fall 2017

date speaker title host(s)
September 11 Mihaela Ifrim (UW) Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation Kim & Tran
September 18 Longjie Zhang (University of Tokyo) TBD Angenent
September 22,

VV B239 4:00pm

Jaeyoung Byeon (KAIST) Colloquium: Patterns formation for elliptic systems with large interaction forces Rabinowitz
September 25 Tuoc Phan (UTK) TBD Tran
September 26,

VV B139 4:00pm

Hiroyoshi Mitake (Hiroshima University) Joint Analysis/PDE seminar Tran
September 29,

VV901 2:25pm

Dongnam Ko (CMU & SNU) a joint seminar with ACMS: TBD Shi Jin & Kim
October 2 No seminar due to a KI-Net conference
October 9 Sameer Iyer (Brown University) TBD Kim
October 16 Jingrui Cheng (UW) TBD Kim & Tran
October 23 Donghyun Lee (UW) TBD Kim & Tran
October 30 Myoungjean Bae (POSTECH) TBD Feldman
November 6 Jingchen Hu (USTC and UW) TBD Kim & Tran

Abstracts

Mihaela Ifrim

Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation

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.

Jaeyoung Byeon

Title: Patterns formation for elliptic systems with large interaction forces

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.