Lack of the strict dissipativity and modification for the dissipative Bresse system

Abstract

Recently a lot of physical models which possess a complicated dissipative structure are studied. The key point is to analyze the eigenvalues of the corresponding eigenvalue problem for physical models, and the stability condition introduced in [11,12] is one of the important tools to get the detailed information of the eigenvalues. Throughout the stability condition, we find that the Bresse system is not strictly dissipative even if it has any frictional damping. In this situation, we introduce the different types of damping effects and analyze the detailed dissipative structure for the Bresse system.