Polynomial Stabilization of the Heat Equation on the Half‐Line With Locally Distributed Control Using the Conformable Derivative

Source abstract

We study the polynomial stabilization of the heat equation on the half‐line with a locally distributed control, in the framework of the conformable derivative. We show that the stable invariant subspaces generalize naturally and that the stabilization rate becomes t − α ( N + 1/4) . A numerical validation is proposed to illustrate the theoretical results. Perspectives on the optimization of the time‐cost trade‐off for controllability are outlined.