C. A. Raposo

Exponential stability for the Timoshenko system with two weak dampings

In this paper we consider a linear system of Timoshenko type beam equations with frictional dissipative terms. We show the exponential decay of the solution by using a method developed by Z. Liu and S. Zheng and their collaborators in past years. This method is very different from some others in the literature, such as the traditional energy method. It is our hope that the reader will find the method presented in this work is powerful and simple.

Global existence and stability for wave equation of Kirchhoff type with memory condition at the boundary

Abstract We consider a nonlinear wave equation of Kirchhoff type with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

Solution and Asymptotic Behaviour for a Nonlocal Coupled System of Reaction-Diffusion

This paper concerns with the existence, uniqueness and asymptotic behaviour of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and exponential decay of solutions by the classic energy method. We improve the results obtained by Chipot-Lovato and Menezes for coupled systems. A numerical scheme is presented.

Exponential stability for a structure with interfacial slip and frictional damping

Abstract In this work we prove the exponential stability for a laminated beam consisting of two identical layers of uniform density, which is a system closely related to the Timoshenko beam theory, taking into account that an adhesive of small thickness is bonding the two layers and produce the interfacial slip. It is assumed that the thickness of the adhesive bonding the two layers is small enough so that the contribution of its mass to the kinetic energy of the entire beam may be ignored.

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.

Global solution for a thermoelastic system with p-Laplacian

Abstract In this work we prove global solution for the nonlinear system u t t − Δ p u + θ = | u | r − 1 u θ t − Δ θ = u t where Δ p is the nonlinear p -Laplacian operator, 2 ≤ p ∞ . We apply the potential well theory. The global solution is constructed by means of the Faedo–Galerkin approximations, taking into account that the initial data is in appropriated set of stability created from the Nehari manifold.

Large-time behaviour of solutions to the equations of one-dimensional nonlinear thermoviscoelasticity with memory

This paper is concerned with the large-time behaviour of globally defined smooth solutions of the initial-boundary value problem for the one-dimensional nonlinear thermoviscoelasticity system with memory.