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In the first part of the talk, we introduce the concept:
Controllability of Differential Equations. Then we give some examples in finite (ODE) and infinite dimensional(PDE) context. We discuss the controllability of Transport and Heat equation. In the second part of the talk, we consider compressible Navier-Stokes equations in one dimension, linearized around a constant steady state (Q_ 0 , V_ 0 ) , with
Q_ 0 > 0, V 0 ≥ 0 . It is a Coupled system of transport and heat type equations. We study the controllability of this linearized system in bounded interval (0, L) with Dirichlet boundary condition or periodic boundary condition. We obtain several interesting positive and negative results for the null controllability and approximate controllability of the system using interior or boundary control in both the cases V_0 = 0 and V _0 > 0. |