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.

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In this paper, we consider a coupled Lamé system of nonlinear viscoelastic equations with general source terms. Under some suitable conditions on the initial data and the relaxation functions, we prove an asymptotic stability result of global solution taking into account that the kernel is not necessarily decreasing.This work generalizes and improves earlier results in the literature. KEYWORDS coupled system, Lamé system, Lyapunov function, viscoelastic term MSC CLASSIFICATION 35L70; 35B40; 76Exx Δ e u = Δu + ( + ) ∇ (div u) , u = (u 1 , u 2 , u 3 ) T , Math Meth Appl Sci.wileyonlinelibrary.com/journal/mma

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.