Stabilization of semilinear heat equations, with fading memory, by boundary feedbacks

In this paper, we design stabilizing Dirichlet boundary feedback laws for heat equations with fading memory. The linear finite-dimensional controllers are easily manageable from the computational point of view, because of their simple feedback form, involving only the first N∈NN∈N eigenfunctions of the Laplace operator. Two examples are provided at the end of the paper, in order to illustrate the acquired results.