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<identifier>oai:HAL:hal-00803214v1</identifier>
<datestamp>2018-01-11</datestamp>
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<title lang=en>A second-order differential system with hessian-driven damping; application to non-elastic shock laws</title>
<creator>Attouch, Hedy</creator>
<creator>Maingé, Paul-Emile</creator>
<creator>Redont, Patrick</creator>
<contributor>Institut de Mathématiques et de Modélisation de Montpellier (I3M) ; Université Montpellier 2 - Sciences et Techniques (UM2) - Université de Montpellier (UM) - Centre National de la Recherche Scientifique (CNRS)</contributor>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>Differential Equations & Applications</source>
<identifier>hal-00803214</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00803214</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00803214/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00803214/file/Attouch-Mainge-Redont-30August2011.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00803214</source>
<source>Differential Equations & Applications, 2012, 4 (1), pp.27-65</source>
<language>en</language>
<subject lang=en>viscoelastic membrane.</subject>
<subject lang=en>asymptotic stabilization</subject>
<subject lang=en>convex variational analysis</subject>
<subject lang=en>dissipative dynamical systems</subject>
<subject lang=en>exponential stabilization</subject>
<subject lang=en>gradient-like systems</subject>
<subject lang=en>Hessian-driven damping</subject>
<subject lang=en>impact dynamics</subject>
<subject lang=en>nonelastic shocks</subject>
<subject lang=en>nonsmooth potentials</subject>
<subject lang=en>restitution coefficient</subject>
<subject lang=en>second-order nonlinear differential equations</subject>
<subject lang=en>unilateral mechanics</subject>
<subject lang=en>viscoelastic membrane</subject>
<subject>[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>We consider a second-order differential system with Hessian-driven damping . An interesting property of this system is that, after introduction of an auxiliary variable y , it can be equivalently written as a first-order system in time and space. This allows us to extend the analysis to the case of a convex lower semicontinuous potential and so to introduce constraints in the model. When considering the indicator function of a closed convex set, the subdifferential operator takes account of the contact forces. In this setting, by playing with the geometrical damping parameter, we can describe nonelastic shock laws with restitution coefficient. Taking advantage of the infinite dimensional framework, we introduce a nonlinear hyperbolic PDE describing a damped oscillating system with obstacle. The system is dissipative; in the convex case each trajectory weakly converges to a minimizer of the global potential energy function. Exponential stabilization is obtained under strong convexity assumptions.</description>
<date>2012-02-01</date>
</dc>
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