Speaker: Dr. Debanja Mitra
Affiliation: Department of Mathematics, IIT Bombay
Date and Time: 6 July 2023 1130 AM
Title: Lack of null controllability of certain linear transport-parabolic coupled systems.
Abstract: In my talk, I shall discuss the control aspects of linear coupled transport-parabolic systems with variable coefficients in one space dimension. The systems are considered with homogeneous Dirichlet boundary conditions and with localized interior controls acting on both transport and parabolic equations.We show that coupled systems are not null controllable at small time. This time depends on the transport velocity and the support of the controls. When the transport velocity is identically zero, the systems are not null controllable at any time. To achieve these results, we construct highly localized solutions, known as Gaussian beams, corresponding to the adjoint systems, and using them, we show that the corresponding observability inequalities fail. However, these systems are null controllable at any time by controls acting everywhere in the parabolic equation, under suitable assumptions on the initial data and the coefficients.
This a joint work with S. Ahamed and D. Maity published as ‘Lack of null controllability of one dimensional linear coupled transport-parabolic system with variable coefficients’, Journal of Differential Equations (2022), Vol. 320, pp. 64-113.