On Some Recent Advances on Stabilization for Hyperbolic Equations

Intrinsic Decay Rate Estimates for Semilinear Abstract Second Order Equations with Memory

“…It should be noted that techniques used in [2] and the present manuscript are very different. While [2] refers to weighted energy inequalities developed in [3][4][5], the present work is based on the ODE method developed in [22]. We believe that this latter method provides a more effective framework when dealing with the case of inequality characterization of the relaxation kernel.…”

“…Under the assumptions imposed later on one shows without difficulties that the system (14.1) has a unique "finite energy" solution .u; u t / 2 C.0; 1; D.A 1=2 H /, which is "regular" for regular initial data. Problems related to long time behavior, including asymptotic behavior have occupied central role in the literature on viscoelastic models [16,30,31] including references therein and more recently [1,2,5,17,25,26,28,32] among others Our goal is to study the decay rates of the energy associated with the system (14.1). Precise definition of the energy is given below after introducing notation used throughout the manuscript.…”

Moore–Gibson–Thompson equation with memory, part I: exponential decay of energy

“…Moore-Gibson-Thompson (MGT) equation arises from modeling high frequency ultrasound waves. Without memory, the linearized MGT equation reads (5) τ u ttt + αu tt + c 2 Au + bAu t = 0.…”

Stability Properties of Coupled Impedance Passive LTI Systems

“…The stability of various specific infinite-dimensional coupled systems has been investigated in a series of papers by J.M. Wang and co-authors, see [16], [45], [46], also by F. Alabau-Boussouira and co-authors [3], [4], S. Hansen and coauthors [17], [18], and our paper [56]. Many further references on coupled systems can be found in these works.…”