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Decay property of regularity-loss type for quasi-linear hyperbolic systems of viscoelasticity

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  • In this paper, we consider a quasi-linear hyperbolic systems of viscoelasticity. This system has dissipative properties of the memory type and the friction type. The decay property of this system is of the regularity-loss type. To overcome the difficulty caused by the regularity-loss property, we employ a special time-weighted energy method. Moreover, we combine this time-weighted energy method with the semigroup argument to obtain the global existence and sharp decay estimate of solutions under the smallness conditions and enough regularity assumptions on the initial data.
    Mathematics Subject Classification: Primary: 35D30, 35L52; Secondary:74D10.

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