| Title:
|
Stability of vibrations for some Kirchhoff equation with dissipation (English) |
| Author:
|
Nandi, Prasanta Kumar |
| Author:
|
Gorain, Ganesh Chandra |
| Author:
|
Kar, Samarjit |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
205-215 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Kirchhoff equation |
| Keyword:
|
dissipation |
| Keyword:
|
vibration |
| Keyword:
|
stabilization |
| Keyword:
|
energy decay estimate |
| MSC:
|
35B35 |
| MSC:
|
35L70 |
| MSC:
|
37L15 |
| MSC:
|
45K05 |
| idZBL:
|
Zbl 06362222 |
| idMR:
|
MR3183473 |
| DOI:
|
10.1007/s10492-014-0050-x |
| . |
| Date available:
|
2014-03-20T08:23:16Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143630 |
| . |
| Reference:
|
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| Reference:
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