Classical Controllability for the Semilinear Parabolic Equations with Superlinear Terms

Abstract

AbstractIn this chapter we establish the global approximate controllability of the semilinear heat equation with superlinear term, governed in a bounded domain by a pair of controls: (I) the traditional internal either locally distributed or lumped control and (II) the lumped control entering the system as a time-dependent coefficient. The motivation for the latter is due to the well known lack of global controllability properties for this class of pde’s when they are steered solely by the former controls. Our approach involves an asymptotic technique allowing us to separate and combine the impacts generated by the above-mentioned two types of controls. In particular, the addition of multiplicative control allows us to reduce the use of the additive one to the local controllability technique only.KeywordsMultiple SolutionIrrational NumberControl PairClassical ControllabilityApproximate ControllabilityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.