This article is available for purchase or by subscription. See below.
Abstract
|
Under suitable growth and coercivity conditions on the nonlinear damping operator
which ensure
nonresonance, we estimate the ultimate bound of the energy of the general solution to the
equation
,
,
where
is a positive selfadjoint operator on a Hilbert space
and
is a bounded forcing term
with values in
. In general
the bound is of the form
,
where
stands
for the
norm of
with values in
and the growth of
does not seem to
play any role. If
behaves like a power for large values of the velocity, the ultimate bound has quadratic growth with
respect to
and this
result is optimal. If
is antiperiodic, we obtain a much lower growth bound and again the result is shown
to be optimal even for scalar ODEs.
|
PDF Access Denied
We have not been able to recognize your IP address
52.14.240.252
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
second-order equation, nonlinear damping, energy bound,
antiperiodic
|
Mathematical Subject Classification 2010
Primary: 34A34, 34D20, 35B40, 35L10, 35L90
|
Milestones
Received: 25 August 2017
Revised: 30 October 2017
Accepted: 14 November 2017
Published: 26 January 2018
|
|