Differential and Integral Equations
- Differential Integral Equations
- Volume 15, Number 1 (2002), 115-128.
Feedback null controllability of the semilinear heat equation
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.
Differential Integral Equations, Volume 15, Number 1 (2002), 115-128.
First available in Project Euclid: 21 December 2012
Permanent link to this document
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