Margareth S. Alves

Analyticity of Semigroups Associated with Thermoviscoelastic Mixtures of Solids

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a one-dimensional theory of mixtures of thermoviscoelastic solids. Our main goal is to present conditions which insure the analyticity and the lack of analyticity of the corresponding semigroup.

The Lack of Exponential Stability in Certain Transmission Problems with Localized Kelvin--Voigt Dissipation

In this paper we consider the transmission problem of a material composed of three components; one of them is a Kelvin--Voigt viscoelastic material, the second is an elastic material (no dissipation), and the third is an elastic material inserted with a frictional damping mechanism. The main result of this paper is that the rate of decay will depend on the position of each component. When the viscoelastic component is not in the middle of the material, then there exists exponential stability of the solution. Instead, when the viscoelastic part is in the middle of the material, there is not exponential stability. In this case we show that the corresponding solution decays polynomially as

Analyticity and Smoothing Effect for the Coupled System of Equations of Korteweg-de Vries Type with a Single Point Singularity

1/t^{2}

Smoothing properties for the higher-order nonlinear Schrödinger equation with constant coefficients

. Moreover we show that the rate of decay is optimal over the domain of the infinitesimal generator. Finally, using a second order scheme that ensures the decay of energy (Newmark-

Exponential stability of a thermoviscoelastic mixture with second sound

\beta

Transmission Problem in Thermoelasticity

method), we give some numerical examples which demonstrate this asymptotic behavior.

Stabilization of mixture of two rigid solids modeling temperature and porosity

Using Bourgain spaces and the generator of dilation P=3t∂t+x∂x, which almost commutes with the linear Korteweg-de Vries operator, we show that a solution of the initial value problem associated for the coupled system of equations of Korteweg-de Vries type which appears as a model to describe the strong interaction of weakly nonlinear long waves, has an analyticity in time and a smoothing effect up to real analyticity if the initial data only have a single point singularity at x=0.

Smoothing properties for a coupled system of nonlinear evolution dispersive equations

Abstract We study local and global existence and smoothing properties for the initial value problem associated to a higher-order nonlinear Schrodinger equation with constant coefficients which appears as a model for propagation of pulse in an optical fiber.

Stability of a thermoelastic mixture with second sound

ABSTRACT In this work, we consider a one-dimensional model of a thermoviscoelastic mixture with second sound. Under suitable assumption on the constitutive constants of the system, we prove, using the theory of semigroup of linear operators and results obtained by Prüss (1984) and Borichev and Tomilov (2009), that the damping effect through heat conduction given by the Cattaneo law is strong enough to stabilize the system.

About analyticity for the coupled system of linear thermoviscoelastic equations

We show that the energy to the thermoelastic transmission problem decays exponentially as time goes to infinity. We also prove the existence, uniqueness, and regularity of the solution to the system.