Geodesic
Stability of vibrations for some Kirchhoff equation with dissipation
Applications of Mathematics, Tome 59 (2014) no. 2, pp. 205-215
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In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval $[0,T]$ with a tolerance level $\gamma $. The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force $f$. After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances are insignificant.
In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval $[0,T]$ with a tolerance level $\gamma $. The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force $f$. After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances are insignificant.
DOI : 10.1007/s10492-014-0050-x
Classification : 35B35, 35L70, 37L15, 45K05
Keywords: Kirchhoff equation; dissipation; vibration; stabilization; energy decay estimate 
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Nandi, Prasanta Kumar; Gorain, Ganesh Chandra; Kar, Samarjit. Stability of vibrations for some Kirchhoff equation with dissipation. Applications of Mathematics, Tome 59 (2014) no. 2, pp. 205-215. doi: 10.1007/s10492-014-0050-x

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