| Title:
|
Small time-periodic solutions to a nonlinear equation of a vibrating string (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
6 |
| Year:
|
1987 |
| Pages:
|
480-490 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small. (English) |
| Keyword:
|
nonlinear string equation |
| Keyword:
|
accelerated convergence |
| Keyword:
|
existence |
| Keyword:
|
periodic |
| Keyword:
|
Dirichlet boundary conditions |
| Keyword:
|
vibrations |
| Keyword:
|
damped extensive string |
| Keyword:
|
time-periodic solution |
| MSC:
|
35B10 |
| MSC:
|
35L70 |
| MSC:
|
58C15 |
| MSC:
|
73K03 |
| idZBL:
|
Zbl 0653.35063 |
| idMR:
|
MR0916063 |
| DOI:
|
10.21136/AM.1987.104278 |
| . |
| Date available:
|
2008-05-20T18:33:33Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104278 |
| . |
| Reference:
|
[1] R. W. Dickey: Infinite systems of nonlinear oscillation equations with Linear Damping.Siam J. Appl. Math. 19 (1970), pp. 208-214. Zbl 0233.34014, MR 0265654, 10.1137/0119019 |
| Reference:
|
[2] S. Klainerman: Global existence for nonlinear wave equations.Comm. Pure Appl. Math. 33 (1980), pp. 43--101. Zbl 0405.35056, MR 0544044, 10.1002/cpa.3160330104 |
| Reference:
|
[3] P. Krejčí: Hard Implicit Function Theorem and Small periodic solutions to partial differential equations.Comment. Math. Univ. Carolinae 25 (1984), pp. 519-536. MR 0775567 |
| Reference:
|
[4] J. Moser: A rapidly-convergent iteration method and nonlinear differential equations.Ann. Scuola Norm. Sup. Pisa 20-3 (1966), pp. 265-315, 499-535. |
| Reference:
|
[5] O. Vejvoda, et al.: Partial differential equations: Time-periodic Solutions.Martinus Nijhoff Publ., 1982. Zbl 0501.35001 |
| . |
