General decay of solutions of a linear one-dimensional porous-thermoelasticity system with a boundary control of memory type (original) (raw)
Zeitschrift für angewandte Mathematik und Physik, 2012
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Exponential decay in one-dimensional porous-thermo-elasticity
Mechanics Research Communications, 2005
This paper concerns the one dimensional problem of the porous-thermo-elasticity. Two kinds of dissipation process are considered: the viscosity type in the porous structure and the thermal dissipation. It is known that when only thermal damping is considered or when only porous damping is considered we have the slow decay of the solutions. Here we prove that when both kinds of dissipation terms are taken into account in the evolution equations the solutions are exponentially stable.
General stabilization of a thermoelastic systems with a boundary control of a memory type
Studia Universitatis Babes-Bolyai Matematica
In this paper we consider an n-dimensional thermoelastic system, in a bounded domain, where the memory-type damping is acting on a part of the boundary and where the resolvent kernel k of −g (t)/g(0) satisfies k (t) ≥ γ (t) (−k (t)) p , t ≥ 0, 1 < p < 3 2. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. This work generalizes and improves earlier results in the literature.
Well-posedness and general decay of a nonlinear damping porous-elastic system with infinite memory
Journal of Mathematical Physics, 2020
In the present work, we consider a one-dimensional porous-elastic system with infinite memory and a nonlinear damping term. We establish the well-posedness of the system using semigroup theory and show the general decay for the case of nonequal speeds of wave propagation. Introducing some conditions on the kernel of the infinite memory term helps estimate the nonequal speed term even if this complementary control is not strong enough to stabilize the system exponentially. Our result is an extension of many other works in this area.
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ANNALI DELL'UNIVERSITA' DI FERRARA, 2019
In this paper, we consider a one-dimensional porous-elastic system with past history and nonlinear damping term. We established the well-posedness using the semigroup theory and we showed that the dissipation given by this complementary controls guarantees the general stability for the case of equal speed of wave propagation.
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Journal of Mathematical Analysis and Applications, 2011
In this paper we study the asymptotic behavior to an one-dimensional porous-elasticity problem with history. We show the lack of exponential stability when the porous dissipation or the elastic dissipation is absent. And we show the lack of analyticity and exponential stability when the porous viscosity and the elastic dissipation are present.