NDLI: Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems

Content Provider	Springer Nature Link
Author	Alabau Boussouira, Fatiha
Copyright Year	2004
Abstract	This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. Our work completes the work of [15] and improves the results of [21] and [22] (see also [23] and [10]). We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy.
Starting Page	61
Ending Page	105
Page Count	45
File Format	PDF
ISSN	00954616
Journal	Applied Mathematics and Optimization
Volume Number	51
Issue Number	1
e-ISSN	14320606
Language	English
Publisher	Springer-Verlag
Publisher Date	2004-10-15
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Systems Theory, Control Calculus of Variations and Optimal Control Optimization Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization

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