LQR based stabilization of an 1D heat equation with advection and memory effects (opens in new tab)

We derive a one-dimensional model for heat transfer in a moving fluid incorporating Fourier conduction, an exponentially decaying memory term, and advection under thermally insulated boundary conditions. We numerically construct a bounded state feedback law driving the closed-loop solution to zero exponentially with decay rate at least $\omega>0$ for every initial state, i.e., we solve the $\omega$-stabilization problem. We explicitly describe t...