Exact controllability of the superlinear heat equation. (English) Zbl 0964.93046

Barbu, V.

Appl. Math. Optimization 42, No. 1, 73-89 (2000).

The paper studies the internal and boundary null controllability of a parabolic equation with superlinear nonlinearity. It has been proved that under certain conditions on the superlinear nonlinearity term the equation is internal null controllable. This also implies the boundary controllability. The proof is based on Kakutani’s fixed-point theorem and on Carleman estimates for the backward adjoint linearized system.

Reviewer: Sebastian Aniţa (Iaşi)

MSC:

93C20	Control/observation systems governed by partial differential equations
93B05	Controllability
93C10	Nonlinear systems in control theory

Keywords:

heat equation; optimal control; internal and boundary null controllability; parabolic equation; superlinear nonlinearity; Kakutani’s fixed-point theorem; Carleman estimates