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dc.contributor.authorKhapalov, Alexander Y. ( )
dc.contributor.authorNag, Parthasarathi ( Orcid Icon 0000-0001-9502-4029 )
dc.date.accessioned2020-11-25T19:26:01Z
dc.date.available2020-11-25T19:26:01Z
dc.date.issued2003-06-21
dc.identifier.citationKhapalov, A. Y., & Nag, P. (2003). Energy decay estimates for Lienard's equation with quadratic viscous feedback. Electronic Journal of Differential Equations, 2003(70), pp. 1-12.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13010
dc.description.abstractThis article concerns the stabilization for a well-known Lienard's system of ordinary differential equations modelling oscillatory phenomena. It is known that such a system is asymptotically stable when a linear viscous (motion-activated) damping with constant gain is engaged. However, in many applications it seems more realistic that the aforementioned gain is not constant and does depend on the deviation from equilibrium. In this article, we consider a (nonlinear) gain, introduced in [2], which is proportional to the square of such deviation and derive an explicit energy decay estimate for solutions of the corresponding ``damped'' Lienard's system. We also discuss the place of our result in the framework of stabilization of so-called critical bilinear systems.en_US
dc.formatText
dc.format.extent12 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectBilinear systemsen_US
dc.subjectStabilizationen_US
dc.subjectQuadratic feedbacken_US
dc.subjectEnergy decay estimateen_US
dc.titleEnergy decay estimates for Lienard's equation with quadratic viscous feedbacken_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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