Asymptotic behaviour of the energy in partially viscoelastic materials

By Jaime E. Mu nmacr, O. Rivera, A. P. Salvatierra. 2001

133 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/abf87e47e97291fc56d2a282c3d5da9d0c67bf79

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Decay estimates for second order evolution equations with memory (2008, unknown): “Dissipation Extending to the present abstract set-up an idea due to [22], we define the energy of a mild solution u of (12) on a given interval [0, T ] as Eu(t) := 1 2 ∥∥u′(t)∥∥2 + 1 2 ( 1 − t ∫ 0 β(s) ds ∥∥√Au(t)∥∥2 − F (u(t)) + 1 2 t ∫”
General decay of solutions of a nonlinear system of viscoelastic wave equations (2011, background): “[26] showed that solutions decay exponentially to zero, provided the relaxation function decays in a similar fashion, regardless to the size of the viscoelastic part of the material.”
Moore-Gibson-Thompson equation with memory, part II: general decay of energy (2015, unknown): “se where memory eﬀects are incorporated into the model. It is well known that memory generates stabilizing mechanism for second order wave equations. There is an abundant literature on the topic, see [2, 3, 4, 6, 5, 9, 10, 14, 20, 21, 23, 24], to name a few. The prototype model is viscoelastic wave ”
Partial Differential Equations/Optimal Control A general method for proving sharp energy decay rates for memory-dissipative evolution equations (2009, background): “This problem has already been investigated in several papers under different additional assumptions for k (also referred to as the relaxation function), see [13,18,17,11,12,6,3,10,7] and the references therein.”
Attractors for wave equations with degenerate memory (2016, methodology): “For N ≥ 2, when ω satisfies the geometric control condition, the corresponding problem was studied by Muñoz Rivera and Peres Salvatierra [30] in the Euclidean setting and by Cavalcanti et al.”
Intrinsic Decay Rate Estimates for Semilinear Abstract Second Order Equations with Memory (2014, methodology): “1) has been used to model the viscoelastic materials with memory effects and extensively investigated in the literature, see [28, 30, 31].”