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In their paper "Stability to weak dissipative bresse system", Alabau et al.studied the exponential and polynomial stability of the Bresse system with oneglobally distributed dissipation law. Our goal is to extend their results, bytaking into consideration the important case when the dissipation law islocally distributed and to improve the polynomial energy decay rate. We thenstudy the energy decay rate of the Bresse system with one locally internaldistributed dissipation law acting on the equation about the shear angledisplacement. Under the equal speed wave propagation condition, we show thatthe system is exponentially stable. On the contrary, we establish a newpolynomial energy decay rate.

Locally internal stability of weakly elastic Bresse system