中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Jiao He (University of Paris-Saclay)
题 目：Wave-structure interactions in shallow water
时 间：2024.01.22（星期一）14:00-15:00
地 点：思源楼S813
摘 要：In this talk we present a mathematical model of a particular wave energy converter, the so-called oscillating water columns in shallow water regime. This model can be reformulated as two transmission problems. We will show how to derive the transmission conditions and formulate the problem as an IBVP with a semi-linear boundary condition given by an ordinary differential equation. A rigorous well-posedness result of this coupled PDE-ODE will be given as well. Finally, we use the characteristic equations of Riemann invariants to obtain the discretized transmission conditions and show some numerical simulations in the end.
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报告人：Professor Hoai Minh Nguyen (Sorbonne Université)
题 目：Local boundary controllability of the KdV equation
时 间：2024.01.22（星期一）16:00-17:00
地 点：Zoom ID: 924 888 5804 Passcode: AMSS2022
摘 要：In this talk, I report recent progress on the local boundary controllability of the KdV equation in a bounded interval. The focus is on Dirichlet boundary controls on the left, or Dirichlet or Neumann boundary controls on the right. The phenomena depends strongly on the location of the controls. For left controls, the system is always locally controllable in small time. For right controls, the phenomena depends on the length of the interval, which is critical or not. In the non-critical case, the system is locally controllable in small time. In the critical case, the phenomena are complex. It can happen that either the system is locally controllable in small time, or not locally controllable in small time but locally controllable in finite time, or even not locally controllable in any positive time.
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