J.E. Muñoz Rivera

Energy decay for Timoshenko systems of memory type

Abstract Linear systems of Timoshenko type equations for beams including a memory term are studied. The exponential decay is proved for exponential kernels, while polynomial kernels are shown to lead to a polynomial decay. The optimality of the results is also investigated.

Positive solutions for a nonlinear nonlocal elliptic transmission problem

We show the existence and nonexistence of positive solutions for a transmission problem given by a system of two nonlinear elliptic equations of Kirchhoff type.

Polynomial decay for the energy with an acoustic boundary condition

Abstract In this paper, we establish the polynomial decay for the energy of a wave motion in a bounded domain Ω ∋ R 3 with a smooth boundary ∂Ω = Λ , on a part Λ0 of which an acoustic boundary condition in subjected. The multiplicative techniques and energy method are used.

Asymptotic stability of semigroups associated to linear weak dissipative systems

In this work, we consider a class of linear dissipative evolution equations. We showthat the solution of this class has a polynomial rate of decay as time tends to infinity, but does not have exponential decay.

Asymptotic behaviour in n-dimensional thermoelasticity☆

Abstract We study the thermoelastic system and we prove that the divergence of the displacement vector field and the thermal difference decay exponentially as time goes to infinity. Moreover, we show that the decay cannot hold in general.

A boundary condition with memory in elasticity

Abstract In this paper, we study the stability of solutions of the n -dimensional nonhomogeneous and anisotropic elastic system with memory condition working at the boundary. We show that such dissipation is strong enough to produce exponential decay to the solution, provided the relaxation function also decays exponentially.

Hybrid laminated Timoshenko beam

We consider the hybrid laminated Timoshenko beam model. This structure is given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. We suppose that the beam is fastened securely on the left while on the right it’s free and has an attached container. Using the semigroup approach and a result of Borichev and Tomilov, we prove that the solution is polynomially stable.