[00304] Phase transition and control of PDE models in applied sciences
Session Time & Room : 4D (Aug.24, 15:30-17:10) @G801
Type : Proposal of Minisymposium
Abstract : The minisymposium aims to discuss recent developments and applications on phase transition and control for partial differential equations, abbreviated as PDEs, in applied sciences, such as biology, material sciences, engineering and so on.
Partial differential equations are important tools to model and study the various phenomena in applied sciences. The models with phase transition and control issues give rise to a great deal of challenging problems both in theoretical and numerical studies. The sessions focus on the seminal and extensive works in phase transition, boundary stabilization, optimal control of PDE models, such as Keller-Segel model, multi species BGK models, and aggregation models.
[01375] Crowd pressure and turbulence in crowd disasters
Format : Talk at Waseda University
Author(s) :
Liangze Yang (Yanqi Lake Beijing Institute of Mathematical Sciences and Applications)
Abstract : In this study, a mixed-type continuum model for multidirectional pedestrian flow was developed that explicitly
considers the different movement characteristics of pedestrians under different situations: laminar flow in a low-density system and turbulent flow in a high-density system. In addition to the phase transition, the proposed
model can reveal the effects of both force chains and panic sentiment, which are commonly observed phenomena during crowd disasters, by estimating the aggregated pushing pressure.
[01721] Traceability of Water Pollution governed by an Inverse Source Problem
Format : Talk at Waseda University
Author(s) :
Shenwen Yu (Yau Mathematical Sciences Center, Tsinghua University)
Lingyun Qiu (Yau Mathematical Sciences Center, Tsinghua University)
Zhongjing Wang (Department of Hydraulic Engineering, Tsinghua University)
Hui Yu (Yau Mathematical Sciences Center, Tsinghua University)
Abstract : We aim to find the time-dependent source term in the diffusion equation from the boundary measurement. Based on the idea of dynamic complex geometrical optics (CGO) solutions, we analyze a variational formulation of the inverse source problem and prove the uniqueness and stability result. A two-step reconstruction algorithm is proposed, which first recovers the locations of the point sources, and then the emission concentration functions. Some numerical experiments on simulated data are conducted.
[03877] A Cucker-Smale inspired deterministic Mean Field Game with velocity interactions
Format : Talk at Waseda University
Author(s) :
Woojoo Shim (Kyungpook National University)
Filippo Santambrogio (Université Claude Bernard - Lyon 1)
Abstract : In this talk, I would like to introduce a mean field game model for pedestrians moving in a given domain and choosing their trajectories so as to minimize a cost including a penalization on the difference between their own velocity and that of the other agents they meet. During the talk, we will study the existence of an equilibrium in a Lagrangian setting using its variational structure and then study its properties and regularity.
[05554] Provable convergence of blow-up time of numerical approximations for a class of convection-diffusion equations
Format : Online Talk on Zoom
Author(s) :
Yang Yang (Michigan Technological University)
Abstract : In this talk, we investigate the numerical algorithms to capture the blow-up time for a class of convection-diffusion equations with blow-up solutions, such as the chemotaxis model. The blow-up time is difficult to capture since we cannot distinguish whether the blow-up is physical or is due to the instability. We propose two ways to define the numerical blow-up time and prove the convergence to the exact one.
