Marcio V. Ferreira

Stability of a thermoelastic mixture with second sound

We consider the one-dimensional model of a thermoelastic mixture with second sound. We give a complete characterization of the asymptotic properties of the model in terms of the coefficients of the model. We establish the necessary and sufficient conditions for the model to be exponential or polynomial stable and also the conditions for which there exist initial data for where the energy is conserved.

Asymptotic behavior for a generalized micropolar thermoelastic body

Abstract The paper establishes the exponential stability of a micropolar thermoelastic homogeneous and linear body with frictional dissipation and thermal conduction of hyperbolic type, allowing for second sound. Existence and uniqueness are proved within the semigroup framework and stability is achieved thanks to a suitable Lyapunov functional.

Existência e Unicidade de Solução para um sistema de Equações de Maxwell aplicado a um condutor perfeito

Investigaremos questoes relacionadas a existencia e unicidade de solucao para um sistema de equacoes de Maxwell num meio condutor perfeito. Esse estudo sera baseado na caracterizacao dos espacos funcionais de origem eletromagnetica e na aplicacao da teoria de semigrupos de operadores lineares

Existence and Uniqueness of Solution for a System of Maxwell’s Equations in a Perfect Conductor Medium

We investigate, in this paper, questions related to existence and uniqueness of solution for a system of Maxwell’s equations in a perfect conductor medium. This study will be based on the characterization of the functional spaces of electromagnetic origin and application of the theory of semigroups of linear operators. We present results of existence of solution using different techniques from those used by other authors.

ESTABILIDADE DA SOLUÇÃO DA EQUAÇÃO DISSIPATIVA DE BENJAMIN-BONA-MAHONY EM DOMÍNIO COM FRONTEIRA MÓVEL

In this work we consider the Cauchy problem associated to nonlinear and dissipative Benjamin-Bona-Mahony equation in a bounded domain with moving boundary. We prove the existence and uniqueness of global solution and study the asymptotic behavior of the solution. We use the Faedo-Galerkin method, multiplier techniques, energy estimates and compactness for the results.

EXISTENCE, ORTHOGONAL DECOMPOSITION AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF A SYSTEM IN ELECTROMAGNETISM

In this paper we consider a system of Maxwell’s equations, which models the propagation of electromagnetic waves in a bounded region of the space R3. First we prove the existence and uniqueness of solution of such a system using, for this, Semigroup of Linear Operators Theory. We obtain, after this, the orthogonal decomposition of the electromagnetic field. Finally, using that orthogonal decomposition and choosing an appropriate multiplier, we show that the total energy of the system decays exponentially to zero as t → ∞. The method presented in this paper is quite different from those that appear in the literature related to this subject.