Abstract:This paper deals with the asymptotic behavior of a weakly coupled system of two equations in which one of them has a dissipative mechanism given by a memory term. This term depends on the fractional operator with exponent π β [0, 1].We show that strong solutions of the system decay polynomially with a rate that depends on both the exponent π and wave propagation speeds. Optimal decay rates are found and the results show a surprising aspect: More regular damping does not necessarily imply a faster decay.
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