PDE Seminar Fall 2021

Fridays, 2:30 — 3:30pm, Stevenson Center 1312 (in-person) or via Zoom (online).

Date: Friday, Sept. 3rd, 2021.

  • Speaker: Hengrong Du, Vanderbilt University.
  • Title: On hydrodynamics of nematic liquid crystals.
  • Abstract: In this talk, we will report some recent developments on analytic issues on two model PDE systems of hydrodynamics of nematic liquid crystals: the Ericksen—Leslie (EL) system and the Beris—Edwards (BE) system. They are both strongly coupled PDE systems between incompressible Navier–Stokes equations for the background fluid velocity field and gradient-flow-like equations for the order parameter field describing the averaged alignment of liquid crystal molecules. We will include (i) a new concentrated-compactness in 2-D for simplified EL system; (ii) existence and partial regularity in 3-D for co-rotational BE system and general EL with Ginzburg—Landau approximation. This is based on joint works with Tao Huang (Wayne State) and Changyou Wang (Purdue).

Date: Friday, Sept. 10th, 2021.

  • Speaker: Xinyue Zhao, Vanderbilt University.
  • Title: A free boundary tumor growth model with a time delay in cell proliferation.
  • Abstract: Being a leading cause of death, tumor is one of the most important health
    problems facing the whole world. While there is a lot of work on the tumor
    growth models, only a few of them included time delay; and nearly in all the
    literature, only the radially symmetric case was considered with a time delay.
    In this talk, I will present a non-radially symmetric tumor growth model
    with a time delay in cell proliferation. The time delay represents the time taken
    for cells to undergo cell replication (approximately 24 hours). The model is a
    coupled system of an elliptic equation, a parabolic equation and a backward or-
    dinary dierential equation. It incorporates the cell location under the presence
    of time delay, with the tumor boundary as a free boundary. The inclusion of a
    small time delay makes the system non-local, which produces technical dicul-
    ties for the PDE estimates. I will discuss the stability and bifurcation results we
    obtained concerning this model. Through stability analysis, the result indicates
    that tumor with large aggressiveness parameter would trigger instability, which
    is biologically reasonable..

Date: Friday, Oct. 8th, 2021.

  • Speaker: Elena Giorgi, Columbia University.
  • Title: TBA
  • Abstract: TBA

Date: Friday, Oct. 29th, 2021.

  • Speaker: Katrina Morgan, Northwestern University.
  • Title: TBA
  • Abstract: TBA

Date: Friday, Nov. 12th, 2021.

  • Speaker: Federico Pasqualotto, Duke University.
  • Title: TBA
  • Abstract: TBA