Boundary Stabilization of a Thermoelastic Diffusion System of Type II

In this paper we study the boundary stabilization of a one-dimensional thermoelastic diffusion problem of type II. The system of equations is a coupling of three hyperbolic equations. This poses some new mathematical and numerical difficulties. With the help of the semigroup theory of linear operators, we prove the well-posedness of the proposed problem. By using the frequency domain method combined with the multiplier technique, we prove the exponential stability of the solutions. Finally, we present a numerical scheme based on the Chebyshev spectral method and we give two numerical examples to validate the proposed model and to show its capability.