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 ===[[Previous PDE/GA seminars]]===   ===[[Previous PDE/GA seminars]]=== 
−  ===[[Spring 2018  Tentative schedule for Spring 2018]]===  +  ===[[Fall 2019Spring 2020  Tentative schedule for Fall 2019Spring 2020]]=== 
 +  
 +  == PDE GA Seminar Schedule Fall 2018Spring 2019 == 
 +  
   
−  == 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) 
−  
 +  
−  September 11
 +  
−  Mihaela Ifrim (UW)  +   
−  [[#Mihaela Ifrim Wellposedness and dispersive decay of small data solutions for the BenjaminOno equation]]
 +  September 10, 
−   Kim & Tran
 +   Hiroyoshi Mitake (University of Tokyo) 
−  
 +  [[#Hiroyoshi Mitake  TBA ]] 
−  September 18  +  
−  Longjie Zhang (University of Tokyo)  +  
−  [[#Longjie Zhang  On curvature flow with driving force starting as singular initial curve in the plane]]  +  
−   Angenent
 +  
−  
 +  
−  September 22,
 +  
−  VV 9th floor hall, 4:00pm
 +  
−  Jaeyoung Byeon (KAIST)
 +  
−  [[#Jaeyoung Byeon Colloquium: Patterns formation for elliptic systems with large interaction forces]]
 +  
−   Rabinowitz
 +  
−  
 +  
−  September 25
 +  
−   Tuoc Phan (UTK)
 +  
−  [[#Tuoc Phan  CalderonZygmund regularity estimates for weak solutions of quasilinear parabolic equations with an application]]
 +  
  Tran    Tran 
−    +   
−  September 26,  +  September 17, 
−  VV B139 4:00pm
 +   Changyou Wang (Purdue) 
−   Hiroyoshi Mitake (Hiroshima University)  +  [[#Changyou Wang  TBA ]] 
−  [[#Hiroyoshi Mitake  Joint Analysis/PDE seminar: Derivation of multilayered interface system and its application]]  +  
  Tran    Tran 
−    +   
−  September 29,  +  September 24/26, 
−  VV901 2:25pm
 +   Gunther Uhlmann (UWash) 
−   Dongnam Ko (CMU & SNU)  +  [[#Gunther Uhlmann  TBA ]] 
−  [[#Dongnam Ko  a joint seminar with ACMS: On the emergence of local flocking phenomena in CuckerSmale ensembles ]]  +   Li 
−   Shi Jin & Kim  +   
−    +  October 1, 
−  October 2  +   Matthew Schrecker (UW) 
−   No seminar due to a KINet conference  +  [[#Matthew Schrecker  TBA ]] 
−    +   Kim and Tran 
−    +   
−    +  October 8, 
−  October 9  +   Anna Mazzucato (PSU) 
−   Sameer Iyer (Brown University)  +  [[#Anna Mazzucato  TBA ]] 
−  [[#Sameer Iyer  Globalinx Steady Prandtl Expansion over a Moving Boundary ]]  +   Li and Kim 
 +   
 +  October 15, 
 +   Lei Wu (Lehigh) 
 +  [[#Lei Wu  TBA ]] 
  Kim    Kim 
−    +   
−  October 16  +  October 22, 
−   Jingrui Cheng (UW)  +   Annalaura Stingo (UCD) 
−  [[#Jingrui Cheng  A 1D semigeostrophic model with moist convection ]]  +  [[#Annalaura Stingo  TBA ]] 
−   Kim & Tran  +   Mihaela Ifrim 
−    +   
−  October 23
 +  October 29, 
−   Donghyun Lee (UW)
 +   Jessica Lin (McGill University) 
−  [[#Donghyun Lee  The VlasovPoissonBoltzmann system in bounded domains ]]
 +  [[#Jessica Lin  TBA ]] 
−   Kim & Tran
 +  
−  
 +  
−  October 30  +  
−   Myoungjean Bae (POSTECH)  +  
−  [[#Myoungjean Bae  3D axisymmetric subsonic flows with nonzero swirl for the compressible EulerPoisson system ]]
 +  
−   Feldman
 +  
−  
 +  
−  November 6
 +  
−   Jingchen Hu (USTC and UW)
 +  
−  [[#Jingchen Hu  Shock Reflection and Diffraction Problem with Potential Flow Equation ]]
 +  
−   Kim & Tran
 +  
−  
 +  
−  November 20
 +  
−   Xiaoqin Guo (UW)
 +  
−  [[#Xiaoqin Guo  Quantitative homogenization and Harnack inequality for a degenerate discrete nondivergence form random operator ]]
 +  
−   Kim & Tran
 +  
−  
 +  
−  November 27 (special time: 34PM)
 +  
−   RuYu Lai (Minnesota)
 +  
−  [[#RuYu Lai  Inverse problems for Maxwell's equations and its application ]]
 +  
−   Li
 +  
−  
 +  
−  December 4
 +  
−   Norbert Pozar (Kanazawa University)
 +  
−  [[#Norbert Pozar  Viscosity solutions for the crystalline mean curvature flow ]]  +  
  Tran    Tran 
 +   
 +  November 5, 
 +   Albert Ai (University of Berkeley) 
 +  [[#Albert Ai  TBA ]] 
 +   Mihaela Ifrim 
 +   
 +  December 10, 
 +   ( ) 
 +  [[#  TBA ]] 
 +   
     
−  December 5/6 (Wednesday), Colloquium  +  January 28, 
−   Ryan Hynd (U Penn)  +   ( ) 
−  [[#Ryan Hynd  TBD ]]  +  [[#  TBA ]] 
−    +   
−    +   
−  December 11 (Monday), Colloquium  +  March 4 
−   Connor Mooney (ETH Zurich)  +   Vladimir Sverak (Minnesota) 
−  [[#Connor Mooney TBD ]]  +  [[#Vladimir Sverak  TBA(Wasow lecture) ]] 
−    +   Kim 
 +   
 +  March 18, 
 +   Spring recess (Mar 1624, 2019) 
 +  [[#  ]] 
 +   
 +   
 +  April 29, 
 +   ( ) 
 +  [[#  TBA ]] 
 +   
 }   } 
   
−  ==Abstracts==  +  == Abstracts == 
−   +  
−  ===Mihaela Ifrim===
 +  
−   +  
−  Wellposedness and dispersive decay of small data solutions for the BenjaminOno equation
 +  
−   +  
−  Our goal is to take a first step toward understanding the long time dynamics of solutions for the BenjaminOno equation. While this problem is known to be both completely integrable and globally wellposed 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 BenjaminOno equation and provide a simpler, selfcontained approach. This is joined work with Daniel Tataru.
 +  
−   +  
−  ===Longjie Zhang===
 +  
−   +  
−  On curvature flow with driving force starting as singular initial curve in the plane
 +  
−   +  
−  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.
 +  
−   +  
−  ===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, jth 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 2component systems, and then the much more complex case of 3component systems.
 +  
−   +  
−   +  
−  ===Tuoc Phan===
 +  
−  CalderonZygmund regularity estimates for weak solutions of quasilinear parabolic equations with an application.
 +  
−   +  
−  Abstract: In this talk, we first introduce a problem on the existence of global time smooth solutions for a system of crossdiffusion equations. We then recall some classical results on regularity theories, and show that to solve our problem, new results on regularity theory estimates of CalderonZygmund type for gradients of solutions to a class of parabolic equations in Lebesgue spaces are required. We then discuss a result on CalderonZygmnud type estimate in the concrete setting to solve our
 +  
−  mentioned problem regarding the system of crossdiffusion equations. The remaining part of the talk will be focused on some new generalized results on regularity gradient estimates for some general class of quasilinear parabolic equations. Regularity estimates for gradients of solutions in Lorentz spaces will be presented. Ideas of the proofs for the results are given.
 +  
−   +  
−  ===Hiroyoshi Mitake===
 +  
−  Derivation of multilayered interface system and its application
 +  
−   +  
−  Abstract: In this talk, I will propose a multilayered interface system which can be formally derived by the singular limit of the weakly coupled system of the AllenCahn equation. By using the level set approach, this system can be written as a quasimonotone degenerate parabolic system. We give results of the wellposedness of viscosity solutions, and study the singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.
 +  
−   +  
−   +  
−  ===Dongnam Ko===
 +  
−  On the emergence of local flocking phenomena in CuckerSmale ensembles
 +  
−   +  
−  Emergence of flocking groups are often observed in many complex network systems. The CuckerSmale model is one of the flocking model, which describes the dynamics of attracting particles. This talk concerns timeasymptotic behaviors of CuckerSmale particle ensembles, especially for monocluster and bicluster flockings. The emergence of flocking phenomena is determined by sufficient initial conditions, coupling strength, and communication weight decay. Our asymptotic analysis uses the Lyapunov functional approach and a Lagrangian formulation of the coupled system. We derive a system of differential inequalities for the functionals that measure the local fluctuations and group separations along particle trajectories. The bootstrapping argument is the key idea to prove the gathering and separating behaviors of CuckerSmale particles simultaneously.
 +  
−   +  
−  ===Sameer Iyer===
 +  
−  Title: Globalinx Steady Prandtl Expansion over a Moving Boundary.
 +  
−   +  
−  Abstract: I will outline the proof that steady, incompressible NavierStokes flows posed over the moving boundary, y = 0, can be decomposed into Euler and Prandtl flows globally in the tangential variable, assuming a sufficiently small velocity mismatch. The main obstacles in the analysis center around obtaining sharp decay rates for the linearized profiles and the remainders. The remainders are controlled via a highorder energy method, supplemented with appropriate embedding theorems, which I will present.
 +  
−   +  
−  ===Jingrui Cheng===
 +  
−   +  
−  A 1D semigeostrophic model with moist convection.
 +  
−   +  
−  We consider a simplified 1D model of semigeostrophic system with moisture, which describes moist convection in a single column in the atmosphere. In general, the solution is noncontinuous and it is nontrivial part of the problem to find a suitable definition of weak solutions. We propose a plausible definition of such weak solutions which describes the evolution of the probability distribution of the physical quantities, so that the equations hold in the sense of almost everywhere. Such solutions are constructed from a discrete scheme which obeys the physical principles. This is joint work with Mike Cullen, together with Bin Cheng, John Norbury and Matthew Turner.
 +  
−   +  
−  ===Donghyun Lee===
 +  
−   +  
−  We construct a unique globalintime solution to the VlasovPoissonBoltzmann system in convex domains with the diffuse boundary condition. Moreover we prove an exponential convergence of distribution function toward the global Maxwellian.
 +  
−   +  
−  ===Myoungjean Bae===
 +  
−   +  
−  3D axisymmetric subsonic flows with nonzero swirl for the compressible EulerPoisson system.
 +  
−   +  
−  I will present a recent result on the structural stability of 3D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler–Poisson system in a cylinder supplemented with nonsmall boundary data. A special Helmholtz decomposition of the velocity field is introduced for 3D axisymmetric flow with a nonzero swirl (=angular momentum density) component. This talk is based on a joint work with S. Weng (Wuhan University, China).
 +  
−   +  
−  ===Jingchen Hu===
 +  
−   +  
−  Shock Reflection and Diffraction Problem with Potential Flow Equation
 +  
−   +  
−  In this talk, we will present our work on nonsymmetric shock reflection and diffraction problem, the equation concerned is potential flow equation, which is a simplification of Euler System, mainly based on the assumption that flow has no vortex. We showed in both nonsymmetric reflection case and diffraction case, that physically admissible solution does not exist. This implies that the formation of vortex is essential to maintain the structural stability of shock reflection and diffraction.
 +  
−   +  
−  ===Xiaoqin Guo===
 +  
−   +  
−  Quantitative homogenization and Harnack inequality for a degenerate discrete nondivergence form random operator.
 +  
−   +  
−  In the ddimensional integer lattice $\mathbb Z^d$, $d\ge 2$, we consider a discrete nondivergence form difference operator
 +  
−  $$
 +  
−  L_a u(x)=\sum_{i=1}^d a_i(x)[u(x+e_i)+u(xe_i)2u(x)]
 +  
−  $$
 +  
−  where $a(x)=diag(a_1(x),..., a_d(x)), x\in\mathbb Z^d$ are random nonnegative diagonal matrices which are identically distributed and independent and with a positive expectation.
 +  
−  A difficulty in studying this problem is that coefficients are allowed to be zero. In this talk, using random walks in random media and its percolative structure, we will present a Harnack inequality and quantitative homogenization result for this random operator. Joint work with N.Berger, M.Cohen and J.D. Deuschel.
 +  
−   +  
−  ===RuYu Lai===
 +  
−   +  
−  Inverse problems for Maxwell's equations and its application.
 +  
−   +  
−  This talk will illustrate the application of complex geometrical optics (CGO) solutions to Maxwell's equations.
 +  
−  First, I will explain the increasing stability behavior of coefficients for Maxwell equations.
 +  
−  In particular, by using CGO solutions, the stability estimate of the conductivity is improving when frequency is growing.
 +  
−  Second, I will describe the construction of new families of accelerating and almost nondiffracting beams for Maxwell's equations.
 +  
−  They have the form of wave packets that propagate along circular trajectories while almost preserving a trasverse intensity profile.
 +  
−   +  
−  ===Norbert Pozar===
 +  
−   +  
   
−  Viscosity solutions for the crystalline mean curvature flow
 +  === === 
   
−  In this talk I will present some recent results concerning the analysis
 +  Title: 
−  of the level set formulation of the crystalline mean curvature flow.
 +  
−  The crystalline mean curvature, understood as the first variation of an
 +  
−  anisotropic surface energy with an anisotropy whose Wulff shape is a
 +  
−  polytope, is a singular quantity, nonlocal on the flat parts of the
 +  
−  crystal surface. Therefore the level set equation is not a usual PDE and
 +  
−  does not fit into the classical viscosity solution framework. Its
 +  
−  wellposedness in dimensions higher than two was an open problem until
 +  
−  very recently. In a joint work with Yoshikazu Giga (U. of Tokyo), we
 +  
−  introduce a new notion of viscosity solutions for this problem and
 +  
−  establish its wellposedness for compact crystals in an arbitrary
 +  
−  dimension, including a comparison principle and the stability with
 +  
−  respect to approximation by a smooth anisotropic mean curvature flow.
 +  