Abstract
This chapter is concerned with the presentation of some basic results on the exact internal and boundary controllability of linear and semilinear parabolic equations on smooth domains of \({\mathbb {R}}^d.\) The exact controllability of linear stochastic parabolic equations with linear multiplicative Gaussian noise is also briefly studied. The main ingredient to exact controllability is the observability inequality for the dual parabolic equations established in Chapter 2.
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