Stability of vibrations for some Kirchhoff equation with dissipation

Prasanta Kumar Nandi; Ganesh Chandra Gorain; Samarjit Kar

Applications of Mathematics (2014)

  • Volume: 59, Issue: 2, page 205-215
  • ISSN: 0862-7940

Abstract

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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 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.

How to cite

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Nandi, Prasanta Kumar, Gorain, Ganesh Chandra, and Kar, Samarjit. "Stability of vibrations for some Kirchhoff equation with dissipation." Applications of Mathematics 59.2 (2014): 205-215. <http://eudml.org/doc/261075>.

@article{Nandi2014,
abstract = {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.},
author = {Nandi, Prasanta Kumar, Gorain, Ganesh Chandra, Kar, Samarjit},
journal = {Applications of Mathematics},
keywords = {Kirchhoff equation; dissipation; vibration; stabilization; energy decay estimate; Kirchhoff equation; dissipation; vibration; stabilization; energy decay estimate},
language = {eng},
number = {2},
pages = {205-215},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability of vibrations for some Kirchhoff equation with dissipation},
url = {http://eudml.org/doc/261075},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Nandi, Prasanta Kumar
AU - Gorain, Ganesh Chandra
AU - Kar, Samarjit
TI - Stability of vibrations for some Kirchhoff equation with dissipation
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 205
EP - 215
AB - 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.
LA - eng
KW - Kirchhoff equation; dissipation; vibration; stabilization; energy decay estimate; Kirchhoff equation; dissipation; vibration; stabilization; energy decay estimate
UR - http://eudml.org/doc/261075
ER -

References

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