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Decay property of regularityloss type for quasilinear hyperbolic systems of viscoelasticity
1.  Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishiku, Fukuoka 8190395, Japan 
References:
[1] 
P. M. N. Dharmawardane, Global solutions and decay property of regularityloss type for quasilinear hyperbolic systems with dissipation,, J. Hyperbolic Differ. Equ. 10 (2013), 10 (2013), 37. Google Scholar 
[2] 
P. M. N. Dharmawardane, T. Nakamura and S. Kawashima, Decay estimates of solutions for quasilinear hyperbolic systems of viscoelasticity,, SIAM J. Math. Anal. 44 (2012), 44 (2012), 1976. Google Scholar 
[3] 
P. M. N. Dharmawardane, T. Nakamura and S. Kawashima, Global solutions to quasilinear hyperbolic systems of viscoelasticity,, Kyoto J. Math. 51 (2011), 51 (2011), 467. Google Scholar 
[4] 
P. M. N. Dharmawardane, J. E. Muñoz Rivera and S. Kawashima, Decay property for second order hyperbolic systems of viscoelastic materials,, J. Math. Anal. Appl. 366 (2010), 366 (2010), 621. Google Scholar 
[5] 
T. Hosono and S. Kawashima, Decay property of regularityloss type and application to some nonlinear hyperbolicelliptic system,, Math. Models Methods Appl. Sci. 16 (2006), 16 (2006), 1839. Google Scholar 
[6] 
T. J. R. Hughes, T. Kato and J. E. Marsden, Wellposed quasilinear secondorder hyperbolic systems with applications to nonlinear elastodynamics and general relativity,, Arch. Rational Mech. Anal. 63 (1976), 63 (1976), 273. Google Scholar 
[7] 
K. Ide, K. Haramoto and S. Kawashima, Decay property of regularityloss type for dissipative Timoshenko system,, Math. Models Methods Appl. Sci. 18 (2008), 18 (2008), 647. Google Scholar 
[8] 
K. Ide and S. Kawashima, Decay property of regularityloss type and nonlinear effects for dissipative Timoshenko system,, Math. Models Meth. Appl. Sci. 18 (2008), 18 (2008), 1001. Google Scholar 
[9] 
Y. Liu and S. Kawashima, Global existence and asymptotic behavior of solutions for quasilinear dissipative plate equation,, Discrete Continuous Dynamical Systems, 29 (2011), 1113. Google Scholar 
[10] 
Y. Liu and S. Kawashima, Decay property for a plate equation with memorytype dissipation,, Kinetic and Related Models, 4 (2011), 531. Google Scholar 
[11] 
Y. Liu and S. Kawashima, Decay property for the Timoshenko system with memorytype dissipation,, Math. Models Meth. Appl. Sci. 22 (2012), 22 (2012). Google Scholar 
[12] 
A. Matsumura, An energy method for the equations of motion of compressible viscous and heatconductive fluids,, MRC Technical Summary Report, 2194 (1981). Google Scholar 
[13] 
J. E. Muñoz Rivera, Asymptotic behaviour in linear viscoelasticity,, Quart. Appl. Math. 52 (1994), 52 (1994), 628. Google Scholar 
[14] 
J. E. Muñoz Rivera, M. G. Naso and F. M. Vegni, Asymptotic behavior of the energy for a class of weakly dissipative secondorder systems with memory,, J. Math. Anal. Appl. 286 (2003), 286 (2003), 692. Google Scholar 
[15] 
Y. Ueda and S. Kawashima, Decay property of regularityloss type for the EulerMaxwell system,, Methods Appl. Anal. 18 (2011), 18 (2011), 245. Google Scholar 
show all references
References:
[1] 
P. M. N. Dharmawardane, Global solutions and decay property of regularityloss type for quasilinear hyperbolic systems with dissipation,, J. Hyperbolic Differ. Equ. 10 (2013), 10 (2013), 37. Google Scholar 
[2] 
P. M. N. Dharmawardane, T. Nakamura and S. Kawashima, Decay estimates of solutions for quasilinear hyperbolic systems of viscoelasticity,, SIAM J. Math. Anal. 44 (2012), 44 (2012), 1976. Google Scholar 
[3] 
P. M. N. Dharmawardane, T. Nakamura and S. Kawashima, Global solutions to quasilinear hyperbolic systems of viscoelasticity,, Kyoto J. Math. 51 (2011), 51 (2011), 467. Google Scholar 
[4] 
P. M. N. Dharmawardane, J. E. Muñoz Rivera and S. Kawashima, Decay property for second order hyperbolic systems of viscoelastic materials,, J. Math. Anal. Appl. 366 (2010), 366 (2010), 621. Google Scholar 
[5] 
T. Hosono and S. Kawashima, Decay property of regularityloss type and application to some nonlinear hyperbolicelliptic system,, Math. Models Methods Appl. Sci. 16 (2006), 16 (2006), 1839. Google Scholar 
[6] 
T. J. R. Hughes, T. Kato and J. E. Marsden, Wellposed quasilinear secondorder hyperbolic systems with applications to nonlinear elastodynamics and general relativity,, Arch. Rational Mech. Anal. 63 (1976), 63 (1976), 273. Google Scholar 
[7] 
K. Ide, K. Haramoto and S. Kawashima, Decay property of regularityloss type for dissipative Timoshenko system,, Math. Models Methods Appl. Sci. 18 (2008), 18 (2008), 647. Google Scholar 
[8] 
K. Ide and S. Kawashima, Decay property of regularityloss type and nonlinear effects for dissipative Timoshenko system,, Math. Models Meth. Appl. Sci. 18 (2008), 18 (2008), 1001. Google Scholar 
[9] 
Y. Liu and S. Kawashima, Global existence and asymptotic behavior of solutions for quasilinear dissipative plate equation,, Discrete Continuous Dynamical Systems, 29 (2011), 1113. Google Scholar 
[10] 
Y. Liu and S. Kawashima, Decay property for a plate equation with memorytype dissipation,, Kinetic and Related Models, 4 (2011), 531. Google Scholar 
[11] 
Y. Liu and S. Kawashima, Decay property for the Timoshenko system with memorytype dissipation,, Math. Models Meth. Appl. Sci. 22 (2012), 22 (2012). Google Scholar 
[12] 
A. Matsumura, An energy method for the equations of motion of compressible viscous and heatconductive fluids,, MRC Technical Summary Report, 2194 (1981). Google Scholar 
[13] 
J. E. Muñoz Rivera, Asymptotic behaviour in linear viscoelasticity,, Quart. Appl. Math. 52 (1994), 52 (1994), 628. Google Scholar 
[14] 
J. E. Muñoz Rivera, M. G. Naso and F. M. Vegni, Asymptotic behavior of the energy for a class of weakly dissipative secondorder systems with memory,, J. Math. Anal. Appl. 286 (2003), 286 (2003), 692. Google Scholar 
[15] 
Y. Ueda and S. Kawashima, Decay property of regularityloss type for the EulerMaxwell system,, Methods Appl. Anal. 18 (2011), 18 (2011), 245. Google Scholar 
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