Differential and Integral Equations

Feedback null controllability of the semilinear heat equation

Mihai Sîrbu

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In this paper we study the null controllability of the semilinear heat equation studying the properties of the minimum energy that one needs to steer an initial state $x$ in $0$. We prove this is locally Lipschitz, and consequently we obtain the expected optimal feedback law. We also characterize the value function as the unique positive viscosity solution (of the corresponding Hamilton--Jacobi equation with singular final data) which tends to $0$ on admissible trajectories, or as the minimal positive viscosity supersolution.

Article information

Differential Integral Equations, Volume 15, Number 1 (2002), 115-128.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93B05: Controllability
Secondary: 35B37 35K55: Nonlinear parabolic equations 49J20: Optimal control problems involving partial differential equations 93C20: Systems governed by partial differential equations


Sîrbu, Mihai. Feedback null controllability of the semilinear heat equation. Differential Integral Equations 15 (2002), no. 1, 115--128. https://projecteuclid.org/euclid.die/1356060886

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