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SUMMARY:On damped second-order gradient systems
DTSTART;VALUE=DATE-TIME:20181112T132000Z
DTEND;VALUE=DATE-TIME:20181112T141000Z
DTSTAMP;VALUE=DATE-TIME:20220128T033500Z
UID:indico-contribution-3349@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pascal Bégout (TSE)\nUsing small deformations of th
e total energy\, as introduced in [31]\, we establish that damped second o
rder gradient systems u′′(t)+γu′(t)+∇G(u(t))=0\, Turn MathJax of
may be viewed as quasi-gradient systems. In order to study the asymptotic
behavior of these systems\, we prove that any (nontrivial) desingularizing
function appearing in KL inequality satisfies φ(s)⩾cs√ whenever the
original function is definable and CC. Variants to this result are given.
These facts are used in turn to prove that a desingularizing function of t
he potential G also desingularizes the total energy and its deformed versi
ons. Our approach brings forward several results interesting for their own
sake: we provide an asymptotic alternative for quasi-gradient systems\, e
ither a trajectory converges\, or its norm tends to infinity. The converge
nce rates are also analyzed by an original method based on a one-dimension
al worst-case gradient system. We conclude by establishing the convergence
of solutions of damped second order systems in various cases including th
e definable case. The real-analytic case is recovered and some results con
cerning convex functions are also derived.\n\nhttps://indico.math.cnrs.fr/
event/3779/contributions/3349/
LOCATION:Toulouse School of Economics Bât S\, amphi MS001
URL:https://indico.math.cnrs.fr/event/3779/contributions/3349/
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