The Nonlinearly Damped Oscillator
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 9, page 231-246
- ISSN: 1292-8119
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topVázquez, Juan Luis. "The Nonlinearly Damped Oscillator." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 231-246. <http://eudml.org/doc/90694>.
@article{Vázquez2010,
abstract = {
We study the large-time behaviour of the
nonlinear oscillator
\[
\hskip-20mm m\,x'' + f(x') + k\,x=0\,,
\]
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 $f(x')= A\,|x'|^\{\alpha-1\}x'$ with
α real, A>0. We characterize the existence and behaviour
of fast orbits, i.e., orbits that stop in finite time.
},
author = {Vázquez, Juan Luis},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Nonlinear oscillator; nonlinear damping;
fast orbits.; nonlinear oscillator; fast ans slow orbits},
language = {eng},
month = {3},
pages = {231-246},
publisher = {EDP Sciences},
title = {The Nonlinearly Damped Oscillator},
url = {http://eudml.org/doc/90694},
volume = {9},
year = {2010},
}
TY - JOUR
AU - Vázquez, Juan Luis
TI - The Nonlinearly Damped Oscillator
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 231
EP - 246
AB -
We study the large-time behaviour of the
nonlinear oscillator
\[
\hskip-20mm m\,x'' + f(x') + k\,x=0\,,
\]
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 $f(x')= A\,|x'|^{\alpha-1}x'$ with
α real, A>0. We characterize the existence and behaviour
of fast orbits, i.e., orbits that stop in finite time.
LA - eng
KW - Nonlinear oscillator; nonlinear damping;
fast orbits.; nonlinear oscillator; fast ans slow orbits
UR - http://eudml.org/doc/90694
ER -
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