A unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi-discretized vibrating damped systems

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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”
Moore-Gibson-Thompson equation with memory, part II: general decay of energy (2015, background): “There is an abundant literature on the topic, see [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], to name a few.”
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].”