Global Controllability of Certain
Nonlinear Partial Differential
Equations:
The Camassa–Holm and BBM–BBM Equations
报告专家：Shirshendu Chowdhury 助理教授（印度科学教育与研究学院）
报告时间：10月13日（周二）下午15:55-16:40
报告地点：数学学院西303
报告摘要：
In this talk, we investigate the global approximate controllability of two nonlinear PDE models: the Camassa–Holm equation and a coupled BBM–BBM Boussinesq system. Our approach is based on the Agrachev–Sarychev method, which exploits large controls acting over small time intervals to establish controllability results for infinite-dimensional nonlinear systems. We first explain the main ideas of this method in the finite-dimensional setting of ordinary differential equations (ODEs) and then discuss its application to nonlinear PDEs. For the Camassa–Holm equation on the periodic domain \(\mathbb{T}\), we establish global approximate controllability in \(H^s(\mathbb{T})\), for \(s>3/2\), in any positive time using a three-dimensional control. Moreover, the control mechanism prevents finite-time blow-up of solutions.We then consider a \(2\times 2\) coupled Boussinesq system of BBM–BBM type on the one-dimensional torus. We prove that both components can be simultaneously steered arbitrarily close to any prescribed target state, in any given positive time, using a single five-dimensional control acting on only one component. As in the Camassa–Holm case, the control also prevents possible finite-time blow-up. These results demonstrate the effectiveness of the Agrachev–Sarychev framework in establishing global approximate controllability for nonlinear PDEs using finite-dimensional controls.
专家简介：
Prof. Shirshendu Chowdhury is an Associate Professor in the Department of Mathematics and Statistics at the Indian Institute of Science Education and Research (IISER) Kolkata, India. He received his Ph.D. in Mathematics from the Tata Institute of Fundamental Research, Centre for Applicable Mathematics (TIFR-CAM), Bengaluru, in 2013. His doctoral thesis, Control of Linearized Compressible Navier–Stokes Equations, was awarded the Harish Chandra Memorial Award for the Best Ph.D. Thesis in Mathematics for 2013–2014. He subsequently held postdoctoral positions at the Institut de Mathématiques de Toulouse, France, before joining IISER Kolkata in 2015. Prof. Chowdhury's research focuses on control theory of partial differential equations (PDEs), particularly the controllability, stabilization, and optimal control of linear and nonlinear coupled PDE systems arising in fluid mechanics and other applications. His research encompasses compressible and incompressible Navier–Stokes equations, viscoelastic flows, reaction–diffusion systems, and nonlinear evolution equations.
邀请人：张旭
