| Title:
|
Oscillations of a nonlinearly damped extensible beam (English) |
| Author:
|
Feireisl, Eduard |
| Author:
|
Herrmann, Leopold |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
6 |
| Year:
|
1992 |
| Pages:
|
469-478 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that any weak solution to a nonlinear beam equation is eventually globally oscillatory, i.e., there is a uniform oscillatory interval for large times. (English) |
| Keyword:
|
oscillations |
| Keyword:
|
nonlinear beam |
| Keyword:
|
weak solution |
| Keyword:
|
uniform oscillatory interval |
| MSC:
|
35B05 |
| MSC:
|
35B40 |
| MSC:
|
35Q20 |
| MSC:
|
35Q99 |
| MSC:
|
73D35 |
| MSC:
|
73K05 |
| MSC:
|
73K12 |
| MSC:
|
74H45 |
| MSC:
|
74K10 |
| idZBL:
|
Zbl 0769.73048 |
| idMR:
|
MR1185802 |
| DOI:
|
10.21136/AM.1992.104525 |
| . |
| Date available:
|
2008-05-20T18:44:37Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104525 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Cazenave T., Haraux A.: Propriétés oscillatoires des solutions de certaines équations des ondes semi-linéaires.C. R. Acad. Sc. Paris 298 Sér. I no. 18 (1984), 449-452. Zbl 0571.35074, MR 0750743 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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[8] Haraux A., Zuazua E.: Super-solutions of eigenvalue problems and the oscillation properties of second order evolution equations.J. Differential Equations 74 (1988), 11-28. Zbl 0654.34018, MR 0949622, 10.1016/0022-0396(88)90015-0 |
| Reference:
|
[9] Herrmann L.: Optimal oscillatory time for a class of second order nonlinear dissipative ODE.preprint. Zbl 0772.34030, MR 1175931 |
| Reference:
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[10] Kopáčková M., Vejvoda O.: Periodic vibrations of an extensible beam.Časopis pro pěstování matematiky 102 (1977), 356-363. MR 0492762 |
| Reference:
|
[11] Kreith K.: Oscillation theory.Lecture Notes in Mathematics 324, Springer Verlag, 1973. Zbl 0258.35001 |
| Reference:
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| Reference:
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[13] Lions J.-L., Magenes E.: Problèmes aux limites non homogènes et applications I.Ch. 3, Sec. 8.4, Dunod, Paris. |
| Reference:
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[14] Lovicar V.: Periodic solutions of nonlinear abstract second order equations with dissipative terms.Časopis pro pěstování matematiky 102 (1977), 364-369. Zbl 0369.34017, MR 0508656 |
| Reference:
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[15] Lunardi A.: Local stability results for the elastic beam equation.SIAM J. Math. Anal. 18 no. 5 (987), 1341-1366. Zbl 0643.35055, MR 0902336 |
| Reference:
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[16] McKenna Walter W.: Nonlinear oscillations in a suspension bridge.Arch. Rational Mech. Anal. 98 (1987), 167-177. MR 0866720, 10.1007/BF00251232 |
| Reference:
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[17] Temam R.: Infinite-dimensional dynamical systems in mechanics and physics, Ch, 2, Sec. 4.1.Applied Mathematical Sciences 68, Springer Verlag, 1988, MR 0953967 |
| Reference:
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| Reference:
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[19] Yoshida N.: On the zeros of solutions of beam equation.Annali Mat. Pura Appl. 151 (1988), 389-398. MR 0964521, 10.1007/BF01762806 |
| Reference:
|
[20] Zuazua E.: Oscillation properties for some damped hyperbolic problems.Houston J. Math. 16 (1990), 25-52. MR 1071264 |
| . |
