Aicha Nemsi, Abdelfeteh Fareh: General decay of the solution of a one dimensional double porous elastic system with memory, 369-390

Abstract:

In this paper, we consider a one dimensional elastic system with two porous structures and memory effects in both porous equations. We prove that the weak dissipation generated by the memory terms produces a general rate of decay depending on the kernels of the memory terms and the coefficients of the system. Our result improves that of [6] obtained in the presence of strong damping and thermal effect. Moreover, the general decay that we obtained generalizes the previous results in the sense that exponential and polynomial rates of decay are only special cases.

Key Words: Double porosity, memory term, exponential stability, general decay.

2010 Mathematics Subject Classification: Primary 35B35, 35B40, 35Q70, 74D10, 74F10.

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