Viscoelastic boundary stabilization for a transmission problem in elasticity

We consider an anisotropic body which is constituted of twodifferent types of materials supporting a memory boundary conditionand we show that its energy decays uniformly as time goes toinfinity with the same rate as the relaxation function g, thatis, the energy decays exponentially when g decays exponentially,and polynomially when g decays polynomially.     

The Transmission Problem of Viscoelastic Waves

In this paper we consider the transmission problem of viscoelastic waves. That is, we study the wave propagations over materials consisting of elastic and viscoelastic components. We show that for this types of materials the dissipation produced by the viscoelastic part is strong enough to produce exponential decay of the solution, no matter how small is its size. We also show that the linear model is well posed.     

Exponential Stability to a Contact Problem of Partially Viscoelastic Materials

In this paper we study models for contact problems of materials consisting of an elastic part (without memory) and a viscoelastic part, where the dissipation given by the memory is effective. We show that the solution of the corresponding viscoelastic equation decays exponentially to zero as time goes to infinity, provided the relaxation function also decays exponentially, no matter how small is the dissipative part of the material.     

A transmission problem with non‐linear internal damping in elasticity

We consider an anisotropic body constituted by two different types of materials: a part is simple elastic while the other has a non‐linear internal damping. We show that the dissipation caused by the damped part is strong enough to produce uniform decay of the energy, more precisely, the energy decays exponentially when the dissipation is linear with respect to the velocity. For a non‐linear class of dissipations we prove that the energy decays polynomially. Copyright © 2003 John Wiley & Sons, Ltd.     

Phosphonic acid functionalized asymmetric phthalocyanines: synthesis, modification of indium tin oxide, and charge transfer

Metalated and free-base A(3)B-type asymmetric phthalocyanines (Pcs) bearing, in the asymmetric quadrant, a flexible alkyl linker of varying chain lengths terminating in a phosphonic acid (PA) group have been synthesized. Two parallel series of asymmetric Pc derivatives bearing aryloxy and arylthio substituents are reported, and their synthesis and characterization through NMR, combustion analysis, and MALDI-MS are described. We also demonstrate the modification of indium tin oxide (ITO) substrates using the PA functionalized asymmetric Pc derivatives and monitoring their electrochemistry. The PA functionalized asymmetric Pcs were anchored to the ITO surface through chemisorption and their electrochemical properties characterized using cyclic voltammetry to investigate the effects of PA structure on the thermodynamics and kinetics of charge transfer. Ionization energies of the modified ITO surfaces were measured using ultraviolet photoemission spectroscopy.     

Frictional versus Kelvin‐Voigt damping in a transmission problem

We consider 2 transmission problems. The first problem has 2 damping mechanisms acting in the same part of the body, one of frictional type and other of Kelvin‐Voigt type. In this case, we show that, even though it has too much dissipation, the semigroup is not exponentially stable. The second problem also has those damping terms but they act in complementary parts of the body. For this case, we show that the semigroup is exponentially stable and it is not analytic.     

Optimal decay for plates with rotational inertia and memory

We study the asymptotic behavior of a linear plate equation with effects of rotational inertia and a fractional damping in the memory term: where and the kernel g is exponentially decreasing. The main result of this work is the polynomial decay of their solutions when . We prove that the solutions decay with the rate and also that the decay rate is optimal. Furthermore, when , we obtain the exponential decay of the solutions.     

Exact decay rates for weakly coupled systems with indirect damping by fractional memory effects

This paper deals with the asymptotic behavior of a weakly coupled system of two equations in which one of them has a dissipative mechanism given by a memory term. This term depends on the fractional operator with exponent $\theta \in [0,1]$. We show that strong solutions of the system decay polynomially with a rate that depends on both the exponent θ and wave propagation speeds. Optimal decay rates are found and the results show a surprising aspect: More regular damping does not necessarily imply a faster decay.