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.
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. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0050-x/

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