Decay of energy for second-order boundary hemivariational inequalities with coercive damping
type: Item
instance of: scholarly article
title: Decay of energy for second-order boundary hemivariational inequalities with coercive damping
zbMATH Open document ID: 1215.35111
author: Piotr Kalita
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2011-01-31T00:00:00Z
review text: The author considers two strongly damped partial differential inclusions \[ 0\in u''(t) + A(t,u'(t)) + Bu(t)+\gamma^*\partial J (\gamma u(t)) \] and \[ 0\in u''(t) + A(t,u'(t)) + Bu(t)+\gamma^*\partial J (\gamma u'(t)). \] In both cases the differential operator \(A\) is nonlinear pseudomonotone and coercive while the differential operator \(B\) is bounded, linear, monotone and symmetric. The multivalued term has the form of Clarke subdifferential of the functional defined on the space of boundary functions and \(\gamma\) is the trace operator. For both cases the conditions are given under which appropriately defined energy tends to zero exponentially as time tends to infinity. The methodology based on Nakao's lemma is used. For the inclusion with multivalued term dependent on \(u'\) it is shown that exponential energy decay occurs for every of possibly many solutions while for the (more difficult) case of inclusion with multivalued term dependent on \(u\) it is shown, basing on an approximation argument, that there exists a solution with exponential energy decay.
reviewed by: Leszek Gasiński
Mathematics Subject Classification ID: 35L85
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 5843283
zbMATH Keywords: exponential decay of energy
zbMATH Keywords: Clarke subdifferential
MaRDI profile type: Publication
full work available at URL: j.na.2010.09.053
OpenAlex ID: W2034771295
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DOI: 10.1016/J.NA.2010.09.053
description: scientific article; zbMATH DE number 5843283