Asymptotics for some nonlinear damped wave equation : finite time convergence versus exponential decay results
Baji, B. ; Cabot, A. ; Díaz, J. I.
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007), p. 1009-1028 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2007__24_6_1009_0,
     author = {Baji, B. and Cabot, A. and D\'\i az, J. I.},
     title = {Asymptotics for some nonlinear damped wave equation : finite time convergence versus exponential decay results},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {24},
     year = {2007},
     pages = {1009-1028},
     doi = {10.1016/j.anihpc.2006.10.005},
     mrnumber = {2371117},
     zbl = {pre05247896},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_6_1009_0}
}

Baji, B.; Cabot, A.; Díaz, J. I. Asymptotics for some nonlinear damped wave equation : finite time convergence versus exponential decay results. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 1009-1028. doi : 10.1016/j.anihpc.2006.10.005. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_6_1009_0/

[1] Adly S., Attouch H., Cabot A., Finite time stabilization of nonlinear oscillators subject to dry friction, in: Alart P., Maisonneuve O., Rockafellar R.T. (Eds.), Progresses in Nonsmooth Mechanics and Analysis, Advances in Mathematics and Mechanics, Kluwer, 2006, pp. 289-304. | MR 2205459

[2] Baji B., Cabot A., An inertial proximal algorithm with dry friction: finite convergence results, Set Valued Anal. 14 (1) (2006) 1-23. | MR 2232455 | Zbl 1102.65063

[3] Bamberger A., Cabannes H., Mouvement d'une corde vibrante soumise à un frottement solide, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 699-702. | MR 618890 | Zbl 0457.73041

[4] Barbu V., Precupanu T., Convexity and Optimization in Banach Spaces, second ed., D. Reidel, Dordrecht, 1986. | MR 860772 | Zbl 0594.49001

[5] Bogolioubov N., Mitropolski I., Les méthodes asymptotiques en théorie des oscillations non linéaires, Gauthier-Villars, Paris, 1962. | MR 158129 | Zbl 0247.34004

[6] Brézis H., Problèmes unilatéraux, J. Math. Pures Appl. 51 (1972) 1-168. | MR 428137 | Zbl 0237.35001

[7] Brézis H., Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Math. Studies, vol. 5, North-Holland, Amsterdam, 1973. | MR 348562 | Zbl 0252.47055

[8] Brogliato B., Nonsmooth Mechanics, second ed., Springer CCES, London, 1999. | Zbl 0917.73002

[9] Cabannes H., Mouvement d'une corde vibrante soumise à un frottement solide, C. R. Acad. Sci. Paris Sér. A-B 287 (1978) 671-673. | MR 514553 | Zbl 0393.70022

[10] Cabannes H., Study of motions of a vibrating string subject to solid friction, Math. Methods Appl. Sci. 3 (1981) 287-300. | MR 657297 | Zbl 0474.73073

[11] A. Cabot, Stabilization of oscillators subject to dry friction: finite time convergence versus exponential decay results, Trans. Amer. Math. Soc., in press. | MR 2341995 | Zbl 1133.34008

[12] Cazenave T., Haraux A., An introduction to Semilinear Evolution Equations, Oxford Lecture Series in Mathematics and its Applications, vol. 13, 1998. | MR 1691574 | Zbl 0926.35049

[13] Dafermos C.M., Slemrod M., Asymptotic behavior of non linear contraction semi-groups, J. Funct. Anal. 12 (1973) 97-106. | MR 346611 | Zbl 0267.34062

[14] J.I. Díaz, V. Millot, Coulomb friction and oscillation: stabilization in finite time for a system of damped oscillators, in: XVIII CEDYA: Congress on Differential Equations and Applications/VIII CMA: Congress on Applied Mathematics, Tarragona, 2003.

[15] Hale J.K., Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs, vol. 25, Amer. Math. Soc., Providence, RI, 1988. | MR 941371 | Zbl 0642.58013

[16] A. Haraux, Opérateurs maximaux monotones et oscillations forcées non linéaires, Thèse, Université Pierre et Marie Curie, Paris, 1978.

[17] Haraux A., Comportement à l'infini pour certains systèmes dissipatifs non linéaires, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979) 213-234. | MR 559667 | Zbl 0429.35013

[18] Haraux A., Nonlinear Evolution Equations. Global Behavior of Solutions, Lecture Notes in Mathematics, vol. 841, Springer-Verlag, New York, 1981. | MR 610796 | Zbl 0461.35002

[19] Haraux A., Systèmes dynamiques dissipatifs et applications, RMA, vol. 17, Masson, Paris, 1991. | MR 1084372 | Zbl 0726.58001

[20] Panagiotopoulos P.D., Inequality Problems in Mechanics and Applications, Birkhäuser, Boston, 1985. | MR 896909 | Zbl 0579.73014

[21] Rockafellar R.T., Wets R., Variational Analysis, Springer, Berlin, 1998. | MR 1491362 | Zbl 0888.49001

[22] Temam R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, vol. 68, Springer-Verlag, New York, 1988. | MR 953967 | Zbl 0662.35001