In this work, we consider a linear thermoelastic laminated timoshenko beam with distributed delay, where the heat conduction is given by cattaneoâs law. we establish the well posedness of the system. For stability results, we prove exponential and polynomial stabilities of the system for the cases of equal and nonequal speeds of wave propagation.

In this paper, we consider a swelling porous elastic system with a viscoelastic damping and distributed delay terms in the second equation. The coupling gives new contributions to the theory associated with asymptotic behaviors of swelling porous elastic soils. The general decay result is established by the multiplier method.

As a continuity to the study by T. A. Apalarain[3], we consider a one-dimensional porous-elastic system with the presence of both memory and distributed delay terms in the second equation. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result given in Theorem 2.1.

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In this paper, we consider a nonlinear viscoelastic Kirchhoff equation with the presence of both distributed delay term, Balakrishnan‐Taylor damping, and logarithmic nonlinearity. We describe a exponential decay of solutions, and we obtained the asymptotic stability result of the global solution. This study is a continuation of Boulaaras's works (Math. Meth. Appl. Sci. 2019;42:4795– 4814 and Alex. Eng. J. 2020;59:1059–1071)