Controls insensitizing the norm of the solution of a semilinear heat equation. (English) Zbl 0852.35070

Bodart, Olivier; Fabre, Caroline

J. Math. Anal. Appl. 195, No. 3, 658-683 (1995).

The authors consider a semilinear heat equation with partially known initial and boundary conditions. It is shown that the so-called insensitivity conditions are equivalent to a particular nonlinear exact controllability problem for parabolic equations. Solving the linear problem leads to the proof of a non-trivial uniqueness property which is also used to characterize a particular subset of the admissible controls. This characterization is made thanks to a convex duality theorem and allows the authors to use a fixed-point theorem and get the result for the nonlinear case.

Reviewer: G.Sviridyuk (Chelyabinsk)

MSC:

35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
34G20	Nonlinear differential equations in abstract spaces

Keywords:

semilinear heat equation; controllability