| Title:
|
A mathematical model of suspension bridges (English) |
| Author:
|
Liţcanu, Gabriela |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
39-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the existence of weak T-periodic solutions for a nonlinear mathematical model associated with suspension bridges. Under further assumptions a regularity result is also given. (English) |
| Keyword:
|
suspension bridges |
| Keyword:
|
periodic solution |
| Keyword:
|
Galerkin approximation |
| Keyword:
|
Leray-Schauder principle |
| MSC:
|
35A35 |
| MSC:
|
35B10 |
| MSC:
|
35Q72 |
| MSC:
|
70K30 |
| MSC:
|
74H45 |
| MSC:
|
74K10 |
| idZBL:
|
Zbl 1099.74037 |
| idMR:
|
MR2032147 |
| DOI:
|
10.1023/B:APOM.0000024519.46627.4f |
| . |
| Date available:
|
2009-09-22T18:16:38Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134557 |
| . |
| Reference:
|
[1] J. M. Ball: Initial-boundary value problems for an extensible beam.J. Math. Anal. Appl. 42 (1973), 61–90. Zbl 0254.73042, MR 0319440, 10.1016/0022-247X(73)90121-2 |
| Reference:
|
[2] Q. H. Choi, T. Jung: On periodic solutions of the nonlinear suspension bridge equation.Differ. Integral Equ. 4 (1991), 383–396. MR 1081189 |
| Reference:
|
[3] P. Drábek: Jumping nonlinearities and mathematical models of suspension bridges.Acta Math. et Inf. Univ. Ostraviensis 2 (1994), 9–18. MR 1309060 |
| Reference:
|
[4] P. Drábek, H. Leinfelder, and G. Tajčová: Coupled string-beam equations as a model of suspension bridges.Appl. Math. 44 (1999), 97–142. MR 1667633, 10.1023/A:1022257304738 |
| Reference:
|
[5] N. Krylová: Periodic solutions of hyperbolic partial differential equation with quadratic dissipative term.Czechoslovak Math. J. 20(95) (1970), 375–405. MR 0283358 |
| Reference:
|
[6] A. C. Lazer, P. J. McKenna: Large amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis.SIAM Rev. 32 (1990), 537–578. MR 1084570, 10.1137/1032120 |
| Reference:
|
[7] P. J. McKenna, W. Walter: Nonlinear oscillations in a suspension bridge.Arch. Ration. Mech. Anal. 98 (1987), 167–177. MR 0866720, 10.1007/BF00251232 |
| Reference:
|
[8] P. J. McKenna, W. Walter: Travelling waves in a suspension bridge.SIAM J. Appl. Math. 50 (1990), 703–715. MR 1050908, 10.1137/0150041 |
| Reference:
|
[9] L. Sanchez: Periodic solutions of a nonlinear evolution equation with a linear dissipative term.Rend. Sem. Mat. Univ. Politec. Torino 37 (1980), 183–191. Zbl 0459.35009, MR 0608937 |
| Reference:
|
[10] G. Tajčová: Mathematical models of suspension bridges.Appl. Math. 42 (1997), 451–480. MR 1475052, 10.1023/A:1022255113612 |
| Reference:
|
[11] E. Zeidler: Nonlinear Functional Analysis and Its Applications, Vol. I–III.Springer-Verlag, New York, 1985–1990. |
| . |
