In this work, we consider the thermoelastic system with a nonlinear distributed delay. Under appropriate hypothesis on the weight function of the delay we prove well-posedness by using the Feado- Galerkin method. Also we establish an exponential decay result by introducing a suitable Lyapunov functional.

In this paper, we investigated the vibration control of a satellite with two symmetric flexible panels attached with center body. The panels are modeled as transmission Euler-Bernoulli beam. We have proved the well-posedness by using semigroup theory. By applying a control force at the center body of the spacecraft, we established exponential decay result using the multiplier method. The theory is illustrated by a numerical example.