We consider the Bresse system with frictional dissipative terms acting in all the equations. We show the exponential decay of the solution by using a method developed by Z. Liu and S. Zheng and their collaborators in past years. The numerical computations were made by using the finite difference method to prove the theoretical results. In particular, the finite difference method in our case is locking free.
"Numerical Exponential Decay to Dissipative Bresse System." J. Appl. Math. 2010 1 - 17, 2010. https://doi.org/10.1155/2010/848620