## Differential and Integral Equations

### Feedback null controllability of the semilinear heat equation

Mihai Sîrbu

#### 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