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Stability of vibrations for some Kirchhoff equation with dissipation

Prasanta Kumar NandiGanesh Chandra GorainSamarjit Kar — 2014

Applications of Mathematics

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 γ . 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....

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