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

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
Mots clés : nonlinear oscillator, nonlinear damping, fast orbits
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     pages = {231--246},
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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. http://www.numdam.org/articles/10.1051/cocv:2003006/

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