Boundary null-controllability of 1-d linearized
compressible Navier-Stokes System
by one Dirichlet control force
报告专家：Shirshendu Chowdhury博士（Indian Institute of Science Education and Research Kolkata）
报告时间：7月11日（星期五)下午3:00-4:00
报告地点：数学学院西303
报告摘要：
In the first part of this talk, we introduce the concept: Controllability of Differential Equations. Then we give some examples in finite (ODE) and infinite dimensional (PDE) contexts. We recall the controllability results of the Transport and Heat equation. In the second part, we consider compressible Navier-Stokes equations in one dimension, linearized around a positive constant steady state. It is a coupled system of transport (for density) and heat type (for velocity) equations. We study the boundary null-controllability of this linearized system in an interval when a Dirichlet control function is acting either only on the density or only on the velocity component at one end of the interval. In this setup, we state some new control results. We see that these controllability results are optimal/sharp concerning the regularity of initial states (in the velocity case) and time (in the density case). The proof is based on a spectral analysis and on solving a mixed parabolic-hyperbolic moments problem and a parabolic hyperbolic joint Ingham-type inequality. This is a joint work with Kuntal Bhandari, Rajib Dutta and Jiten Kumbhakar. Finally, our talk ends with some ongoing and future directions of research.
邀请人：张旭
