Abstract
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.
Keywords
- Multiple Solution
- Irrational Number
- Control Pair
- Classical Controllability
- Approximate Controllability
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© 2010 Springer-Verlag Berlin Heidelberg
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Khapalov, A.Y. (2010). Classical Controllability for the Semilinear Parabolic Equations with Superlinear Terms. In: Controllability of Partial Differential Equations Governed by Multiplicative Controls. Lecture Notes in Mathematics(), vol 1995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12413-6_5
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DOI: https://doi.org/10.1007/978-3-642-12413-6_5
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12412-9
Online ISBN: 978-3-642-12413-6
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