This paper is concerned with the well‐posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III. We first obtain the well‐posedness of the system by using semigroup method. We then investigate the asymptotic behaviour of the system through the perturbed energy method. We prove that the energy of system decays exponentially in the case of equal wave speeds and decays polynomially in the case of nonequal wave speeds. Under the case of nonequal wave speeds, we also investigate the lack of exponential stability of the system.

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In this paper, we consider a one-dimensional thermoelastic-Bresse system with a delay term, where the heat conduction is given by Cattaneo's law effective in the shear angle displacement. We prove that the system is well-posed by using the semigroup method, and show, using the multiplier method, that the dissipation induced by the heat is strong enough to exponentially stabilize the system in the presence of a "small" delay when the stable number is zero.

Some companions of Ostrowski's inequality for complex functions defined on the unit circle are proved. Our results in special cases not only recapture known results, but also give a smaller estimator than that of the known results. Applications to a composite quadrature rule and to functions of unitary operators in Hilbert spaces are also considered.

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III. We first give the well-posedness of the system by using the semigroup method. Then, we show that the system is exponentially stable under the assumption of equal wave speeds. Furthermore, it is proved that the system is lack of exponential stability for case of nonequal wave speeds. In this regard, a polynomial stability result is proved.