General Decay Rates for a Laminated Beam with Memory

Lack of exponential decay for a laminated beam with structural damping and second sound

In previous work (Z. Angew. Math. Phys. 68(2), 2017), Apalara considered a onedimensional thermoelastic laminated beam under Cattaneo’s law of heat conduction and proved the exponential and polynomial decay results depend on the stability number χτ . In this paper, we continue to study the same system and show that the solution of the concerned system lacks of exponential decay result in the ca...

On the Stabilization for Laminated Beam with Infinite Memory and Different Speeds of Wave Propagation

In this work, we consider a one-dimensional laminated beam in the case of non-equal wave speeds with only one infinite memory on the effective rotation angle. In this case, we establish the general decay result for the energy of solution without any kind of internal or boundary control. The main result is obtained by applying the method used in Guesmia et al. (Electron. J. Differential Equation...

Decay rates for solutions of a system of wave equations with memory ∗ Mauro

The purpose of this article is to study the asymptotic behavior of the solutions to a coupled system of wave equations having integral convolutions as memory terms. We prove that when the kernels of the convolutions decay exponentially, the first and second order energy of the solutions decay exponentially. Also we show that when the kernels decay polynomially, these energies decay polynomially.

General decay of solutions to a one-dimensional thermoelastic beam with variable coefficients

Uniform Decay Rates of Solutions to a Nonlinear Wave Equation with Boundary Condition of Memory Type

In this article we study the hyperbolic problem (1) where R is a bounded region in Rn whose boundary is partitioned into disjoint sets ro, rl. We prove that the dissipation given by the memory term is strong enough to assure exponential (or polynomial) decay provided the relaxation function also decays exponentially (or polynomially). In both cases the solution decays with the same rate of the ...