PolyU-PDE Distinguished Lecture Series

PolyU OER Collections

This lecture series aims at inviting renowned experts in the field of PDEs and related research areas, such as kinetic theory, to present their recent findings in research. The lectures will begin in 2023 and will be held by Department of Applied Mathematics once a month.

Works (4)

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  • Video 
    ["PolyU-PDE distinguished lecture series: kinetic limits of particle systems"]

    PolyU-PDE distinguished lecture series: kinetic limits of particle systems

    In this lecture I consider the fundamental, challenging and largely unsolved problem of deriving rigorously the most popular kinetic equations, starting from the laws governing the dynamics of microscopic systems. I plan to present classical and recent results, discussing also some present perspectives.
    Event date: 30/3/2023
    Speaker: Prof. Mario Pulvirenti (University of Roma La Sapienza)
    Hosted by: Department of Applied Mathematics

    Subjects:
    Mathematics and Statistics
    Keywords:
    Mathematical models Kinetic theory of gases -- Mathematical models
    Resource Type:
    Video
     
  • Video 
    ["PolyU-PDE distinguished lecture series: reversal in the stationary Prandtl equations"]

    PolyU-PDE distinguished lecture series: reversal in the stationary Prandtl equations

    We investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by regions in which u > O and u < 0. The classical point of view of regarding the Prandtl equations as an evolution equation in x completely breaks down since u changes sign. Instead, we view the problem as a quasilinear, mixed-type, free-boundary problem. This is a joint work with Sameer Iyer.
    Event date: 14/3/2023
    Speaker: Prof. Nader Masmoudi (New York University)
    Hosted by: Department of Applied Mathematics

    Subjects:
    Mathematics and Statistics
    Keywords:
    Fluid dynamics -- Mathematical models
    Resource Type:
    Video
     
  • Video 
    ["PolyU-PDE distinguished lecture series: redistribution of damping and the zero relaxation limit in BV"]

    PolyU-PDE distinguished lecture series: redistribution of damping and the zero relaxation limit in BV

    In the context of hyperbolic systems of balance laws with dissipative source manifesting relaxation, recent pr"Ogress will be reported in the program of passing to the limit, in 1he BV setting, as the relaxation lime tends to zero.
    Event date: 16/2/2023
    Speaker: Prof. Constantine Dafermos (Brown University)
    Hosted by: Department of Applied Mathematics

    Subjects:
    Mathematics and Statistics
    Keywords:
    Relaxation Equilibrium -- Mathematical models Differential equations Hyperbolic
    Resource Type:
    Video
     
  • Video 
    ["PolyU-PDE distinguished lecture series : structured equations in biology; relative entropy, monge-kantorovich distance"]

    PolyU-PDE distinguished lecture series : structured equations in biology; relative entropy, monge-kantorovich distance

    Models arising in biology are often written in terms of Ordinary Differential Equations. The celebrated paper of Kermack-McKendrick (19271, founding mathematical epidemiology, showed the necessity to include parameters in order to describe the state of the individuals, as time elapsed after infection. During the 70s, many mathematical studies were developed when equations are structured by age, size, more generally a physiological trait. The renewal, growth-fragmentation are the more standard equations. The talk will present structured equations, show that a universal generalized relative entropy structure is available in the linear case, which imposes relaxation to a steady state under non-degeneracy conditions. In the nonlinear cases, it might be that periodic solutions occur, which can be interpreted in biological terms, e.g., as network activity in the neuroscience. When the equations are conservation laws, a variant of the Monge-Kantorovich distance (called Fortet-Mourier distance) also gives a general non-expansion property of solutions.
    Event date: 19/1/2023
    Speaker: Prof. Benoît Perthame (Sorbonne University)
    Hosted by: Department of Applied Mathematics

    Subjects:
    Mathematics and Statistics and Biology
    Keywords:
    Biomathematics Equations
    Resource Type:
    Video