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

By Fatiha Alabau-Boussouira. 2005

240 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f6adb53e99d1a164f9594d797c5a116f9684c870

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Citations in the corpus

Asymptotic stability of the wave equation on compact surfaces and locally distributed damping-A sharp result (2008, unknown): “ka [CA-DO-LA], we obtain explicit and optimal decay rates of the energy. The obtained decay rates are optimal, since they are the same as these optimal rates derived in the works of Alabau-Boussouira [ALA] or Toudykov [Tou]. Our paper is organized as follows. Section 2 is concerned with the statemen”
Intrinsic Decay Rate Estimates for Semilinear Abstract Second Order Equations with Memory (2014, methodology): “The announcement of the result in [2] attributes its proof to convexity arguments along with suitable weighted inequalities developed in [3, 4].”
Sharp energy estimates for nonlinearly locally damped PDEs via observability for the associated undamped system (2011, methodology): “Our purpose here is indeed to provide a self-contained, easy and explicit approach based on a general methodology initiated in [2,6], pursued through lower energy estimates and further comparison properties in [5] and to combine it with and stress the importance of quasi-optimal geometric conditions”
Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping–source interaction (2007, methodology): “In fact, [1] provides a very complete and optimal treatment of the decay rates obtained for this class of problems.”
On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source (2009, background): “These decay rate estimates are optimal since, when one can explicit them (see [9]), they are the same as those optimal decay rates derived in the paper due to Alabau-Boussouira [3].”
INDIRECT STABILIZATION OF LOCALLY COUPLED WAVE-TYPE SYSTEMS (2012, methodology): “This geometric assumption was introduced in [26] and further used in [5, 6].”
On a wave equation with supercritical interior and boundary sources and damping terms (2011, background): “While energy decay has been extensively studied for interior sources up to the critical level (see for instance the overviews in [2], [3], [11], [16], [23], [30]), few results are available for boundary sources (still up to the critical order) [12], [14], [22], [28]; and none, to our knowledge, for ”
Decay estimates for second order evolution equations with memory (2008, background): “For more general integral inequalities see also [1,2,13,19].”
Partial Differential Equations/Optimal Control A general method for proving sharp energy decay rates for memory-dissipative evolution equations (2009, methodology): “, the behavior of k at infinity), using a general integral inequality theorem and a method introduced for the first time in [1,2].”