Controllability For A Class Of Heat Equations With Perturbations

This paper is concerned with the controllability problem for a class of heat equations with perturbations. First, approximate controllability for the perturbed system is got by this way that linearizing the system and constructing functional and using dual equation, give the form of control function. Then, the system is linearized by variational approach, the local null controllability is proved by applying a generalized implicit function theorem and combining the good property of the solution mapping. At last, the null controllability of the system is given by using approximate controllability and local null controllability.