The Transmission Problem for Thermoelastic Beams

A transmission problem for beams on nonlinear supports

“…Firstly, the control of some unwanted tangential derivatives on the boundary where the support f is acting. However, it seems that a compacity argument similar to the one in [14] may be used to show exponential decay for q = 1. But polynomial decay for q > 1 seems to be a harder question.…”

Analyticity of transmission problem to thermoelastic plates

“…Of course, from the theory of analytic semigroups, we deduce directly the exponential stability of the solutions of our system, but the case where only one region includes the thermoelastic coupling (for example, only in Ω 1 ) is the most interesting to be considered and was solved satisfactorily by the authors Muñoz Rivera, J. E. and Portillo Oquendo, H. in [9]. This paper is organized as follows.…”

“…For example, in [9], the authors proved that a partial thermoelastic dissipation is enough to stabilize the system exponentially. That is, they considered the model…”

Asymptotic Behavior of Nonlinear Transmission Plate Problem

“…Here we investigate whether the thermal dissipation on a part of the plate is enough to have any stabilization. Exponential stability of the linear problem of this type was established in [3].…”