Oscillations of a nonlinearly damped extensible beam
Feireisl, Eduard ; Herrmann, Leopold
Applications of Mathematics, Tome 37 (1992), p. 469-478 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1992-01-01
Classification:  35B05,  35B40,  35Q20,  35Q99,  73D35,  73K05,  73K12,  74H45,  74K10 
@article{104525,
     author = {Eduard Feireisl and Leopold Herrmann},
     title = {Oscillations of a nonlinearly damped extensible beam},
     journal = {Applications of Mathematics},
     volume = {37},
     year = {1992},
     pages = {469-478},
     zbl = {0769.73048},
     mrnumber = {1185802},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104525}
}

Feireisl, Eduard; Herrmann, Leopold. Oscillations of a nonlinearly damped extensible beam. Applications of Mathematics, Tome 37 (1992) pp. 469-478. http://gdmltest.u-ga.fr/item/104525/

Вall J Initial-boundary value problems for an extensible beam, J. Math. Anal. Appl. 42 (1973), 61-90. (1973) | Article | MR 0319440

Ball J. Stability theory for an extensible beam, J. Differential Equations 14 (1973), 339-418. (1973) | Article | MR 0331921 | Zbl 0247.73054

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. (1984) | MR 0750743 | Zbl 0571.35074

Cazenave T.; Haraux A. Oscillatory phenomena associated to semilinear wave equations in one spatial dimension, Trans. Amer. Math. Soc. 300 (1987), 207-233. (1987) | Article | MR 0871673 | Zbl 0628.35058

Cazenave T.; Haraux A. Some oscillatory properties of the wave equation in several space dimensions, J. Functional Anal. 76 (1988), 87-109. (1988) | Article | MR 0923046 | Zbl 0656.35099

Eisley J. G. Nonlinear vibrations of beams and rectangular plates, Z. Angew. Math. Phys. 15 (1964), 167-175. (1964) | Article | MR 0175375

Feireisl E.; Herrmann L.; Vejvoda O. A Landesman-Lazer type condition and the long time behavior of floating plates, preprint, 1991. (1991) | MR 1309062

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. (1988) | Article | MR 0949622 | Zbl 0654.34018

Herrmann L. Optimal oscillatory time for a class of second order nonlinear dissipative ODE, preprint. | MR 1175931 | Zbl 0772.34030

Kopáčková M.; Vejvoda O. Periodic vibrations of an extensible beam, Časopis pro pěstování matematiky 102 (1977), 356-363. (1977) | MR 0492762

Kreith K. Oscillation theory, Lecture Notes in Mathematics 324, Springer Verlag, 1973. (1973) | Zbl 0258.35001

Kreith K.; Kusano T.; Yoshida N. Oscillation properties on nonlinear hyperbolic equations, SIAM J. Math. Anal. 15 no. 3 (1984). (1984) | Article | MR 0740696

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

Lovicar V. Periodic solutions of nonlinear abstract second order equations with dissipative terms, Časopis pro pěstování matematiky 102 (1977), 364-369. (1977) | MR 0508656 | Zbl 0369.34017

Lunardi A. Local stability results for the elastic beam equation, SIAM J. Math. Anal. 18 no. 5 (987), 1341-1366. | MR 0902336 | Zbl 0643.35055

Mckenna Walter W. Nonlinear oscillations in a suspension bridge, Arch. Rational Mech. Anal. 98 (1987), 167-177. (1987) | MR 0866720

Temam R. Infinite-dimensional dynamical systems in mechanics and physics, Ch, 2, Sec. 4.1, Applied Mathematical Sciences 68, Springer Verlag, 1988, (1988) | MR 0953967

Woinowski-Krieger S. The effect of an axial force on the vibration of hinged bars, J. Appi. Mech. 17 (1950), 35-36. (1950) | MR 0034202

Yoshida N. On the zeros of solutions of beam equation, Annali Mat. Pura Appl. 151 (1988), 389-398. (1988) | Article | MR 0964521

Zuazua E. Oscillation properties for some damped hyperbolic problems, Houston J. Math. 16 (1990), 25-52. (1990) | MR 1071264