Decay property of regularity-loss type forquasi-linear hyperbolic systems of viscoelasticity

Priyanjana M. N. Dharmawardane

doi:10.3934/proc.2013.2013.197

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2013, Volume 2013: 197-206. Doi: 10.3934/proc.2013.2013.197 open access

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

Priyanjana M. N. Dharmawardane^1,

1.
Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395

Received: July 31, 2012

Revised: November 30, 2012

Published: October 2013

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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.

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Mathematics Subject Classification: Primary: 35D30, 35L52; Secondary:74D10.

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References

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