Geodesic
The nonlinearly damped oscillator
ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 231-246

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We study the large-time behaviour of the nonlinear oscillator

mx '' +f(x ' )+kx=0,
where m,k>0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case f(x ' )=A|x ' | α-1 x ' with α real, A>0. We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in finite time.

DOI : 10.1051/cocv:2003006
Classification : 34C15
Keywords: nonlinear oscillator, nonlinear damping, fast orbits 
@article{COCV_2003__9__231_0,
     author = {V\'azquez, Juan Luis},
     title = {The nonlinearly damped oscillator},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {231--246},
     publisher = {EDP-Sciences},
     volume = {9},
     year = {2003},
     doi = {10.1051/cocv:2003006},
     mrnumber = {1966532},
     zbl = {1076.34038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003006/}
}
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Vázquez, Juan Luis. The nonlinearly damped oscillator. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 231-246. doi: 10.1051/cocv:2003006

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