Feedback stabilization of semilinear heat equations (Q1773461)

The authors study the internal feedback stabilization of steady-state solutions to the quasilinear heat equation and the boundary feedback stabilization to the semilinear heat equation. They do not use the local null controllability of the quasilinear heat equation to get the stabilization but approach the stabilization in a different way which is inspired by Lyapunov stability theory for finite-dimensional systems. In a similar way, they obtain a boundary feedback controller which locally exponentially stabilizes to the semilinear heat equation.