Stability to weak dissipative Bresse system
The paper deals with the Bresse system with frictional dissipation working only on the angle displacement. The Bresse system is also known as the circular arch problem. It is given by the coupled system of three second order hyperbolic equations. The authors have proved that, the system is not exponentially stable, in general. Namely, it is shown that the considered system is exponentially stable if and only if the velocities of waves propagations are equals. This never happens in the practice. Thus we never have exponential stability. When the velocities are different, it is proved that the solutions decay polynomially to zero, with rates that depends on the initial data and some relationships between the coefficients. A numerical result to verify the analytical results is suggested.
scientific article; zbMATH DE number 5817871
scientific article