Abstract
We present some recent results on the controllability of Partial Differential Equations. We discuss the different notions of controllability and comment on how feasible they are depending on the nature of the system under consideration. We discuss both the wave and heat equations as model examples of conservative and irreversible systems respectively and we describe the different tools that have been developed to address these problems. We also present some recent results on the controllability of the linear system of thermoelasticity which is the simplest one coupling both the hyperbolic and the parabolic nature of the wave and heat equation respectively.
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