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In this paper we consider a system coupling a wave equation with a heatequation through its boundary conditions. The existence of a small parameter inthe heat equation, as a factor multiplying the time derivative, implies theexistence of different time scales between the constituents of the system. Thissuggests the idea of applying a singular perturbation method to study stabilityproperties. In fact, we prove that this method works for the system understudy. Using this strategy, we get the stability of the system and a Tikhonovtheorem, which allows us to approximate the solution of the coupled systemusing some appropriate uncoupled subsystems.

Stability analysis of a linear system coupling wave and heat equations with different time scales