Geodesic
Oscillations of a nonlinearly damped extensible beam
Applications of Mathematics, Tome 37 (1992) no. 6, pp. 469-478

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/AM.1992.104525
Classification : 35B05, 35B40, 35Q20, 35Q99, 73D35, 73K05, 73K12, 74H45, 74K10
Keywords: oscillations; nonlinear beam; weak solution; uniform oscillatory interval 
Feireisl, Eduard; Herrmann, Leopold. Oscillations of a nonlinearly damped extensible beam. Applications of Mathematics, Tome 37 (1992) no. 6, pp. 469-478. doi: 10.21136/AM.1992.104525
@article{10_21136_AM_1992_104525,
     author = {Feireisl, Eduard and Herrmann, Leopold},
     title = {Oscillations of a nonlinearly damped extensible beam},
     journal = {Applications of Mathematics},
     pages = {469--478},
     year = {1992},
     volume = {37},
     number = {6},
     doi = {10.21136/AM.1992.104525},
     mrnumber = {1185802},
     zbl = {0769.73048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104525/}
}
TY  - JOUR
AU  - Feireisl, Eduard
AU  - Herrmann, Leopold
TI  - Oscillations of a nonlinearly damped extensible beam
JO  - Applications of Mathematics
PY  - 1992
SP  - 469
EP  - 478
VL  - 37
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104525/
DO  - 10.21136/AM.1992.104525
LA  - en
ID  - 10_21136_AM_1992_104525
ER  - 
%0 Journal Article
%A Feireisl, Eduard
%A Herrmann, Leopold
%T Oscillations of a nonlinearly damped extensible beam
%J Applications of Mathematics
%D 1992
%P 469-478
%V 37
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104525/
%R 10.21136/AM.1992.104525
%G en
%F 10_21136_AM_1992_104525

[1] Вall J: Initial-boundary value problems for an extensible beam. J. Math. Anal. Appl. 42 (1973), 61-90. | DOI | MR

[2] Ball J.: Stability theory for an extensible beam. J. Differential Equations 14 (1973), 339-418. | DOI | MR | Zbl

[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. | MR | Zbl

[4] Cazenave T., Haraux A.: Oscillatory phenomena associated to semilinear wave equations in one spatial dimension. Trans. Amer. Math. Soc. 300 (1987), 207-233. | DOI | MR | Zbl

[5] Cazenave T., Haraux A.: Some oscillatory properties of the wave equation in several space dimensions. J. Functional Anal. 76 (1988), 87-109. | DOI | MR | Zbl

[6] Eisley J. G.: Nonlinear vibrations of beams and rectangular plates. Z. Angew. Math. Phys. 15 (1964), 167-175. | DOI | MR

[7] Feireisl E., Herrmann L., Vejvoda O.: A Landesman-Lazer type condition and the long time behavior of floating plates. preprint, 1991. | MR

[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. | DOI | MR | Zbl

[9] Herrmann L.: Optimal oscillatory time for a class of second order nonlinear dissipative ODE. preprint. | MR | Zbl

[10] Kopáčková M., Vejvoda O.: Periodic vibrations of an extensible beam. Časopis pro pěstování matematiky 102 (1977), 356-363. | MR

[11] Kreith K.: Oscillation theory. Lecture Notes in Mathematics 324, Springer Verlag, 1973. | Zbl

[12] Kreith K., Kusano T., Yoshida N.: Oscillation properties on nonlinear hyperbolic equations. SIAM J. Math. Anal. 15 no. 3 (1984). | DOI | MR

[13] Lions J.-L., Magenes E.: Problèmes aux limites non homogènes et applications I. Ch. 3, Sec. 8.4, Dunod, Paris.

[14] Lovicar V.: Periodic solutions of nonlinear abstract second order equations with dissipative terms. Časopis pro pěstování matematiky 102 (1977), 364-369. | MR | Zbl

[15] Lunardi A.: Local stability results for the elastic beam equation. SIAM J. Math. Anal. 18 no. 5 (987), 1341-1366. | MR | Zbl

[16] McKenna Walter W.: Nonlinear oscillations in a suspension bridge. Arch. Rational Mech. Anal. 98 (1987), 167-177. | DOI | MR

[17] Temam R.: Infinite-dimensional dynamical systems in mechanics and physics, Ch, 2, Sec. 4.1. Applied Mathematical Sciences 68, Springer Verlag, 1988, | MR

[18] Woinowski-Krieger S.: The effect of an axial force on the vibration of hinged bars. J. Appi. Mech. 17 (1950), 35-36. | MR

[19] Yoshida N.: On the zeros of solutions of beam equation. Annali Mat. Pura Appl. 151 (1988), 389-398. | DOI | MR

[20] Zuazua E.: Oscillation properties for some damped hyperbolic problems. Houston J. Math. 16 (1990), 25-52. | MR

Cité par Sources :