## Differential and Integral Equations

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

### Feedback null controllability of the semilinear heat equation

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060886

**Mathematical Reviews number (MathSciNet)**

MR1869825

**Zentralblatt MATH identifier**

1035.49002

**Subjects**

Primary: 93B05: Controllability

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

#### Citation

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