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Automatica, ISSN 0005-1098, 12/2015, Volume 62, pp. 51 - 64
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2020, Volume 482, Issue 2, p. 123552
Feng and Apalara (2019) investigated the one-dimensional porous-elastic system with finite memory under the assumptions of equal-speed wave propagations and... 
Decay rate | Porous-elastic system | Memory | Non-equal wave speeds | MATHEMATICS | THERMOELASTICITY | MATHEMATICS, APPLIED | ENERGY | EXPONENTIAL DECAY | SOLIDS | UNIFORM DECAY
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 05/2017, Volume 73, Issue 9, pp. 1975 - 1986
In this paper we consider the energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions. Motivated by... 
Wave equation | Memory boundary conditions | Energy decay rates | DISSIPATION | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | CONVEXITY | UNIFORM DECAY | KIRCHHOFF TYPE | SOURCE-TERM | VISCOELASTIC EQUATION | ASYMPTOTIC STABILITY | BLOW-UP | GENERAL DECAY | Liberalism
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 10/2018, Volume 173, Issue 1, pp. 222 - 241
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2018, Volume 56, Issue 2, pp. 1303 - 1320
In this paper, we investigate the uniform stability of a class of nonlinear acoustic wave motions with boundary and localized interior damping. Here the... 
Wave equation | Uniform decay rates | Stability | Localized interior damping | Acoustic boundary condition | MATHEMATICS, APPLIED | localized interior damping | uniform decay rates | wave equation | acoustic boundary condition | stability | AUTOMATION & CONTROL SYSTEMS
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 05/2018, Volume 75, Issue 9, pp. 3269 - 3282
In this paper, we show the energy decay rate for a von Karman system with a boundary nonlinear delay term. This work is devoted to investigate the influence of... 
von karman system | Nonlinear boundary delay term | Exponential energy decay rate | MEMORY-TYPE | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | STABILITY | LINEAR VISCOELASTIC EQUATION | UNIFORM DECAY | MODEL | DYNAMIC BOUNDARY | TIME-VARYING DELAY | WAVE-EQUATION | GENERAL DECAY
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 10/2015, Volume 70, Issue 8, pp. 1878 - 1886
In this paper we consider a von Karman equation of memory type with clamped boundary condition. We establish a decay result of solutions without imposing the... 
Arbitrary decay rates | Memory | von Karman equation | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | GLOBAL ATTRACTORS | VISCOELASTIC EQUATION | UNIFORM DECAY | PLATE | GENERAL DECAY | Decay rate | Von Karman equation | Boundary conditions | Mathematical models | Polynomials | Decomposition | Derivatives | Clamping
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 12/2014, Volume 65, Issue 6, pp. 1189 - 1206
We consider the Timoshenko model for vibrating beams under effect of two nonlinear and localized frictional damping mechanisms acting on the transverse... 
Uniform decay rate estimates | Engineering | Mathematical Methods in Physics | Locally distributed damping | 35B40 | Theoretical and Applied Mechanics | Timoshenko system | 35L53 | BEAM | MATHEMATICS, APPLIED | STABILIZATION | WAVE-EQUATION | Analysis | Resveratrol | Linear systems | Damping | Decay rate | Asymptotic properties | Nonlinearity | Mathematical models | Rotational | Displacement
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2016, Volume 437, Issue 2, pp. 782 - 815
In this paper, we consider a simplified version of a fluid–structure PDE model which has been of longstanding interest within the mathematical and biological... 
Fluid–structure interaction | Equations of mixed type | Partial differential equations | Uniform stability | Micro-local analysis | Fluid-structure interaction | MATHEMATICS, APPLIED | ENERGY | FEEDBACK-CONTROL | STABILITY | EQUATIONS | COUPLED PDE SYSTEM | MATHEMATICS | REGULARITY | UNIFORM STABILIZATION | BOUNDARY DISSIPATION | WEAK SOLUTIONS
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 05/2017, Volume 73, Issue 10, pp. 2293 - 2318
In this paper, we obtain very general decay rate estimates associated to a wave–wave transmission problem subject to a nonlinear damping locally distributed... 
Wave–wave transmission problem | Uniform decay rates | Numerical analysis | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | GLOBAL EXISTENCE | BOUNDARY-CONDITIONS | STABILIZATION | Wave-wave transmission problem | SEMILINEAR WAVE-EQUATION | EVOLUTION-EQUATIONS | SHARP RESULT | CRITICAL EXPONENT | ASYMPTOTIC STABILITY | COMPACT MANIFOLDS | Analysis
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 05/2012, Volume 218, Issue 18, pp. 9085 - 9094
In this paper we study the von Kármán plate model with long-range memory and boundary nonlinear feedback. We establish an explicit and general decay rate... 
General decay rate | Von Kármán system | Convexity | Boundary damping | Viscoelastic | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | STABILIZATION | STABILITY | UNIFORM DECAY | Von Karman system | NONLINEAR VISCOELASTIC EQUATION | WAVE-EQUATION | PLATE | GENERAL DECAY | Damping | Nonlinear feedback | Decay rate | Computation | Feedback | Mathematical analysis | Mathematical models | Boundaries
Journal Article
Nonlinearity, ISSN 0951-7715, 07/2018, Volume 31, Issue 9, pp. 4031 - 4064
We consider the semilinear wave equation posed in an inhomogeneous medium Omega with smooth boundary partial derivative Omega subject to a nonlinear damping... 
Wave equation | nonlinear damping damping | uniform decay rates | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | STABILIZATION | wave equation | WELL-POSEDNESS | PHYSICS, MATHEMATICAL | SHARP RESULT | EXACT CONTROLLABILITY | BOUNDARY | ASYMPTOTIC STABILITY | WEAK SOLUTIONS | ENERGY DECAY | COMPACT MANIFOLDS
Journal Article
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2018, Volume 2018, Issue 24, pp. 1 - 28
This paper is concerned with the internal exact controllability of the following model of dynamical elasticity equations for incompressible materials with a... 
Incompressible materials | Uniform decay rates | Non linear damping | Internal exact controllability | MATHEMATICS | non linear damping | MATHEMATICS, APPLIED | incompressible materials | COMPACT SURFACES | uniform decay rates | STABILIZATION | internal exact controllability | SEMILINEAR WAVE-EQUATION | ASYMPTOTIC STABILITY | ENERGY DECAY | DOMAINS
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 04/2014, Volume 31, pp. 46 - 51
We consider a weak viscoelastic beam equation with internal time-varying delay By introducing suitable energy and Lyapunov functionals, we establish general... 
Weak viscoelasticity | General decay rate | Time-varying delay | Beam equation | MATHEMATICS, APPLIED | STABILITY | UNIFORM DECAY | TERM | FEEDBACKS | SYSTEMS | WAVE-EQUATION | BOUNDARY | EXTENSIBLE BEAM | GENERAL DECAY
Journal Article
Journal of Integral Equations and Applications, ISSN 0897-3962, 2018, Volume 30, Issue 3, pp. 377 - 415
In this work, we are concerned with uniform stabilization for an initial-boundary value problem associated with the Kirchhoff type wave equation with feedback... 
Energy decay rates | Kirchhoff type wave equation | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | MEMORY TERM | STABILIZATION | UNIFORM DECAY | MATHEMATICS | EXTERIOR DOMAINS | energy decay rates | VARIABLE-COEFFICIENTS | NONLINEAR DISSIPATION | SYSTEMS | ASYMPTOTIC STABILITY
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2014, Volume 257, Issue 5, pp. 1501 - 1528
Of concern is the Cauchy problem for coupled second order semilinear evolution equations in a Hilbert space, with indirect memory-damping. We find an approach... 
Second order evolution equations | Coupled system | Uniform decay | Memory effect | Indirect damping | Optimal rate | MATHEMATICS | VOLTERRA EQUATION | SYSTEMS | VISCOELASTIC EQUATION | KERNELS
Journal Article
Electronic Journal of Differential Equations, ISSN 1072-6691, 07/2017, Volume 2017, Issue 161, pp. 1 - 12
We study a class of wave propagation problems concerning the nonlinearity of dynamic evolution for boundary material. We establish an observability inequality... 
Coupled boundary equations | Uniform decay rates | Observability inequality | Nonlinear wave | MATHEMATICS | MATHEMATICS, APPLIED | uniform decay rates | observability inequality | EVOLUTION-EQUATIONS | coupled boundary equations
Journal Article
Applicable Analysis, ISSN 0003-6811, 08/2018, Volume 97, Issue 11, pp. 1916 - 1932
In this paper we deal with a nonlinear extensible viscoelastic beam model whose memory term is considered in a history setting. The goal is to extend an... 
decay rates | well-posedness | 35B35 | 74D99 | 35B40 | Extensible beams | viscoelastic models | 35L76 | EXISTENCE | MATHEMATICS, APPLIED | ENERGY | EXPONENTIAL STABILITY | TIMOSHENKO SYSTEMS | UNIFORM DECAY | SEMIGROUPS | ASYMPTOTIC STABILITY | DISSIPATIVE SYSTEMS | EQUATION | GENERAL DECAY | Viscoelasticity | Extensibility | Stability | Decay rate | Beams (structural)
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 12/2014, Volume 55, Issue 12, p. 121504
In this paper, we are concerned with the asymptotic behaviour of weak solutions to the initial boundary value problem for a class of quasilinear hyperbolic... 
EXISTENCE | DISSIPATION | ENERGY | THEOREMS | VISCOELASTIC EQUATION | EVOLUTION-EQUATIONS | UNIFORM DECAY | PHYSICS, MATHEMATICAL | DAMPED WAVE-EQUATION | ASYMPTOTIC-BEHAVIOR | Damping | Boundary value problems | Decay rate | Asymptotic properties | Mathematical analysis | Decay | Strain
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 351, Issue 2, pp. 522 - 535
In this paper, we consider a model of nonlinear viscoelastic shallow shell that is referred to as the full Marguerre–von Kármán under the presence of long-time... 
Nonlinear | Uniform decay | Marguerre–von Kármán equations | Viscoelastic | Marguerre-von Kármán equations | SYSTEM | DISSIPATION | MATHEMATICS, APPLIED | SHELL EQUATIONS | STABILIZATION | MATHEMATICS | ASYMPTOTIC ANALYSIS | Marguerre-von Karman equations | BOUNDARY | PLATE
Journal Article
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