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Energy decay to Timoshenko system with indefinite damping
Author(s) -
Fatori Luci H.,
Saito Tais O.,
Sepúlveda Mauricio,
Takahashi Renan
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5861
Subject(s) - mathematics , sign (mathematics) , displacement (psychology) , function (biology) , mathematical analysis , vibration , exponential function , rod , viscous damping , physics , acoustics , medicine , psychology , alternative medicine , pathology , evolutionary biology , psychotherapist , biology
We consider the classical Timoshenko system for vibrations of thin rods. The system has an indefinite damping mechanism, ie, it has a damping function a = a ( x ) possibly changing sign, present only in the equation for the vertical displacement. We shall prove that exponential stability depends on conditions regarding of the indefinite damping function a and a nice relationship between the coefficient of the system. Finally, we give some numerical result to verify our analytical results.