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

Pages: 197 - 206, Issue special, November 2013

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Priyanjana M. N. Dharmawardane - Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan (email)

Abstract: 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.

Keywords:  Viscoelasticity, dissipative terms, time-weighted energy method, semigroup argument, decay property.
Mathematics Subject Classification:  Primary: 35D30, 35L52; Secondary:74D10.

Received: August 2012;      Revised: December 2012;      Published: November 2013.