Energy decay to Timoshenko's system with thermoelasticity of type III

Article type: Research Article

Authors: Fatori, L.H.^; | Muñoz Rivera, J.E. | Nunes Monteiro, R.

Affiliations: Department of Mathematics, Universidade Estadual de Londrina, Campus Universitário, Londrina, CEP 86.051-990, Paraná, Brazil. E-mails: lucifatori@uel.br, rodrigonunesmonteiro@hotmail.com | National Laboratory of Scientific Computations, LNCC/MCT, Rua Getúlio Vargas 333, Quitandinha, Petrópolis, CEP 25651-070, RJ, Brazil and Instituto de Matemática – UFRJ, Av. Horácio Macedo, Centro de Tecnologia Cidade Universitária – Ilha do Fundão, 21941-972 Rio de Janeiro, RJ, Brasil. E-mail: rivera@lncc.br

Note: [] Corresponding author. E-mail: lucifatori@uel.br

Abstract: We consider the thermoelastic beam system when the oscillations are defined by the Timoshenko's model and the heat conduction is given by Green and Naghdi theories. Our main result is that the corresponding semigroup is exponentially stable if and only if the wave speeds associated to the hyperbolic part of the system are equal. In the case of lack of exponential stability we show that the solution decays polynomially and we prove that the rate of decay is optimal.

Keywords: Timoshenko system, decay rates, optimality of polynomial stability

DOI: 10.3233/ASY-131196

Journal: Asymptotic Analysis, vol. 86, no. 3-4, pp. 227-247, 2014