In this paper, we investigate a coupled system modeled by fluid and thermoelastic plate while the heat effects are modeled by the Cattaneo' law giving rise to a ``second sound" effect. By using the semigroup method, we prove the well-posedness of the system. Then, we construct the second order energy to control the term ∥∇θ∥L2(Г0) so as to establish the exponential decay of the solutions by using the modified multipliers method.
2010 Mathematics Subject Classification: 35Q30, 74F05, 74F10.