Null Controllability with Constraints on the State for the Semilinear Heat Equation

G. Massengo Mophou () and O. Nakoulima
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G. Massengo Mophou: Université des Antilles et de La Guyane
O. Nakoulima: Université des Antilles et de La Guyane

Journal of Optimization Theory and Applications, 2009, vol. 143, issue 3, No 7, 539-565

Abstract: Abstract We consider a null controllability problem for the semilinear heat equation with finite number of constraints on the state. Interpreting each constraint by means of adjoint state notion, we transform the linearized problem into an equivalent linear problem of null controllability with constraint on the control. Using inequalities of observability adapted to the constraint, we solve the equivalent problem. Then, by a fixed-point method, we prove the main result.

Keywords: Systems governed by PDEs; Nonlinear PDEs of parabolic type; Null controllability; Carleman inequalities; Observability inequality (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-009-9568-6

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