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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Classical Controllability for the Semilinear Parabolic Equations with Superlinear Terms
verfasst von : Alexander Y. Khapalov
Erschienen in: Controllability of Partial Differential Equations Governed by Multiplicative Controls
Verlag: Springer Berlin Heidelberg
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In 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.