2013, 2013(special): 197-206. doi: 10.3934/proc.2013.2013.197

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

1. 

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

Received  August 2012 Revised  December 2012 Published  November 2013

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.
Citation: Priyanjana M. N. Dharmawardane. Decay property of regularity-loss type for quasi-linear hyperbolic systems of viscoelasticity. Conference Publications, 2013, 2013 (special) : 197-206. doi: 10.3934/proc.2013.2013.197
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show all references

References:
[1]

J. Hyperbolic Differ. Equ. 10 (2013), 37-76.  Google Scholar

[2]

SIAM J. Math. Anal. 44 (2012), 1976-2001.  Google Scholar

[3]

Kyoto J. Math. 51 (2011), 467-483.  Google Scholar

[4]

J. Math. Anal. Appl. 366 (2010), 621-635.  Google Scholar

[5]

Math. Models Methods Appl. Sci. 16 (2006), 1839-1859.  Google Scholar

[6]

Arch. Rational Mech. Anal. 63 (1976), 273-294.  Google Scholar

[7]

Math. Models Methods Appl. Sci. 18 (2008), 647-667.  Google Scholar

[8]

Math. Models Meth. Appl. Sci. 18 (2008), 1001-1025.  Google Scholar

[9]

Discrete Continuous Dynamical Systems, A 29 (2011), 1113-1139.  Google Scholar

[10]

Kinetic and Related Models, 4 (2011), 531-547.  Google Scholar

[11]

Math. Models Meth. Appl. Sci. 22 (2012), 1150012, 19 pp.  Google Scholar

[12]

MRC Technical Summary Report, Univ. of Wisconsin-Madison \#2194 (1981). Google Scholar

[13]

Quart. Appl. Math. 52 (1994), 628-648.  Google Scholar

[14]

J. Math. Anal. Appl. 286 (2003), 692-704.  Google Scholar

[15]

Methods Appl. Anal. 18 (2011), 245-267.  Google Scholar

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