Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 向圣权 博士，école Polytechnique Fédérale de Lausanne
| | Inviter: | | Title:
| Finite time stabilization of the heat equation | Time & Venue:
| 2021.05.28 16:00-17:00 南楼N204室 | Abstract:
| 腾讯会议：654 425 155
Stability is a natural decay phenomenon typically dues to dissipation of systems, while stabilization is an artificial process to stabilize those unstable systems via controls. It finds application to rockets, traffic road, open channel of the river, even Covid-19.
We talk about the stabilization problem of the heat equation whose controllability property is known for decades, Lebeau-Robbiano (1995) and Fursikov-Imanuvilov (1996). The finite time stabilization of the 1D model was discovered by Coron-Nguyen (2015), while the same question for multidimensional cases remained open. Inspired by Coron-Trélat (2004) we introduce the “frequency Lyapunov approach” that allows us to stabilize the heat equation exponentially with large decay rate with explicit feedback laws, where the spectral inequality using microlocal analysis is naturally adapted leading to quantitative estimates. By further constructing explicit feedback laws we solve the finite time stabilization problem. This method also works for Navier-Stokes equations.
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