PDE Seminar Fall 2017

Fridays, 4:10pm, Stevenson Center 1307

Date: Friday, September 8, 2017.

  • Speaker: Wandi Ding, Middle Tennessee State University.
  • Title: Optimal Control applied to Elliptic and Parabolic PDEs with Biological Applications.
  • Abstract: We apply the optimal control theory to Elliptic and Parabolic partial differential equations. We study the control problem of maximizing the net benefit in the conservation of a single species with a fixed amount of resources. We also consider an optimal control problem of a system of parabolic partial differential equations modelling the competition between an invasive and a native species. The existence of an optimal control is established and the uniqueness and characterization of the optimal control are investigated for both applications. Numerical simulations illustrate several cases. Some open problems are discussed.

Date: Friday, September 15, 2017.

  • Speaker: Nemanja Kosovalic, University of South Alabama.
  • Title: Self-Excited Periodic and Quasi-Periodic Vibrations for Higher
    Dimensional Damped Wave Equations.
  • Abstract: Using techniques from local bifurcation theory, we prove the existence of various types of temporally periodic and quasi-periodic waves for damped wave and beam equations, in higher dimensions. The emphasis is on understanding the role of external bifurcation parameters and symmetry, in generating the periodic/quasi-periodic motion of interest. Most of the work presented is joint with Brian
    Pigott.

Date: Friday, September 22, 2017.

  • Speaker: Gieri Simonett, Vanderbilt University.
  • Title: Maximal regularity and critical spaces for quasilinear parabolic evolution equations.
  • Abstract: In this talk, I will review some recent results concerning the topics listed in the title.
    Applications to problems in fluid dynamics will be mentioned.

Date: Friday, October 6, 2017.

  • Speaker: Glenn Webb, Vanderbilt University.
  • Title: Spatial Spread of Epidemic Diseases in Geographical Settings: Seasonal Influenza Epidemics in Puerto Rico.
  • Abstract: Deterministic models are developed for the spatial spread of epidemic diseases in geographical settings. The models are focused on outbreak that arise from a small number of infected hosts imported into sub-regions of the geographical settings. The goal is to understand how spatial heterogeneity influences the transmission dynamics of the susceptible and infected populations. The models consist of systems of partial differential equations with diffusion terms describing the spatial spread of the underlying microbial infectious agents. Applications are given to seasonal influenza epidemics in Puerto Rico.

Date: Friday, Oct 20, 2017 (meeting at SC 1206).

  • Speaker: Yixiang Wu, Vanderbilt University.
  • Title: TBA.
  • Abstract: TBA.

Date: Friday, Oct 27, 2017.

  • Speaker: Zehua Zhao, Johns Hopkins University.
  • Title: TBA.
  • Abstract: TBA.

Date: Friday, Dec 1, 2017.

  • Speaker: Rares Rasdeaconu, Vanderbilt University.
  • Title: TBA.
  • Abstract: TBA.