Internal controllability of parabolic equations with inputs in coefficients

Abstract

Very often, the input control arises in the coefficients of a parabolic equation and the exact controllability of initial data to origin or to a given stationary state is a delicate problem which cannot be treated by the linearization method developed in the previous chapter. However, in some situations, one can construct explicit feedback controllers which steer initial data to a given stationary state. In general, such a controller is nonlinear, eventually multivalued mapping, and its controllability effect is based on the property of solutions to certain nonlinear partial differential equations to have extinction in finite time. Here we shall study a few examples of this type.