Arched beams of Bresse type: New thermal couplings and pattern of stability

Article type: Research Article

Authors: Bittencourt Moraes, G.E.^a | de Camargo, S.J.^b | Jorge Silva, M.A.^{b; *}

Affiliations: [a] Department of Mathematics, State University of Maringá, Maringá 87020-900, Paraná, Brazil | [b] Department of Mathematics, State University of Londrina, Londrina 86057-970, Paraná, Brazil

Correspondence: [*] Corresponding author. E-mail: marcioajs@uel.br.

Abstract: This is the second paper of a trilogy intended by the authors in what concerns a unified approach to the stability of thermoelastic arched beams of Bresse type under Fourier’s law. Differently of the first one, where the thermal couplings are regarded on the axial and bending displacements, here the thermal couplings are taken over the shear and bending forces. Such thermal effects still result in a new prototype of partially damped Bresse system whose stability results demand a proper approach. Combining a novel path of local estimates by means of the resolvent equation along with a control-observability analysis developed for elastic non-homogeneous systems of Bresse type proposed in trilogy’s first paper, we are able to provide a unified methodology of the asymptotic stability results, by proving the pattern of them with respect to boundary conditions and the action of temperature couplings, which is in compliance with our previous and present goal.

Keywords: Bresse system, thermoelasticity, stability, optimality

DOI: 10.3233/ASY-231850

Journal: Asymptotic Analysis, vol. 135, no. 1-2, pp. 157-183, 2023