Applications of Mathematics

, Volume 59, Issue 2, pp 205–215 | Cite as

Stability of vibrations for some Kirchhoff equation with dissipation

  • Prasanta Kumar NandiEmail author
  • Ganesh Chandra Gorain
  • Samarjit Kar


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.


Kirchhoff equation dissipation vibration stabilization energy decay estimate 

MSC 2010

35B35 35L70 45K05 37L15 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  • Prasanta Kumar Nandi
    • 1
    Email author
  • Ganesh Chandra Gorain
    • 2
  • Samarjit Kar
    • 1
  1. 1.Department of MathematicsNational Institute of TechnologyDurgapurIndia
  2. 2.Department of MathematicsJ.K.CollegePuruliaIndia

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