Yanni Zeng . LARGE TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR VISCOELASTIC MODEL WITH FADING MEMORY[J]. Acta mathematica scientia, Series B, 2012 , 32(1) : 219 -236 . DOI: 10.1016/S0252-9602(12)60014-9

[1] Bianchini S, Hanouzet B, Natalini R. Asymptotic behavior of smooth solutions for partially dissipative
hyperbolic systems with a convex entropy. Comm Pure Appl Math, 2007, 60(11): 1559–1622

[2] Cole J D. On a quasi-linear parabolic equation occurring in aerodynamics. Quart Appl Math, 1951, 9: 225–236

[3] Dafermos C M, Nohel J A. Energy methods for nonlinear hyperbolic Volterra integrodi?erential equations.
Comm Partial Di?er Equ, 1979, 4: 219–278

[4] Dafermos C M, Nohel J A. A nonlinear hyperbolic Volterra equation in viscoelasticity//Clark D N, Pecelli
G, Sacksteder R, eds. Contributions to Analysis and Geometry: Supplement to the American Journal of
Mathematics. Baltimore, London: The Johns Hopkins University Press, 1981: 87–116

[5] Georgiev V, Rubino B, Sampalmieri R. Global existence for elastic waves with memory. Arch Ration Mech
Anal, 2005, 176(3): 303–330

[6] Hopf E. The partial di?erential equation ut +uux = μuxx. Comm Pure Appl Math, 1950, 3: 201–230

[7] Hrusa W, Nohel J. The cauchy problem in one-dimensional nonlinear viscoelasticity. J Differ Equ, 1985,
59: 388–412

[8] Kawashima S. Large-time behavior of solutions to hyperbolic-parabolic systems of conservation laws and
applications. Proc Roy Soc Edinburgh, 1987, 106A(1/2): 169–194

[9] Liu T -P. Nonlinear stability of shock waves for viscous conservation laws. Mem Am Math Soc, 1985, 328:
1–108

[10] Liu T -P. Nonlinear waves for viscoelasticity with fading memory. J Differ Equ, 1988, 76: 26–46

[11] Liu T -P, Zeng Y. Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of
conservation laws. Mem Am Math Soc, 1997, 125(599): viii+120 pp

[12] Liu T -P, Zeng Y. Compressible Navier-Stokes equations with zero heat conductivity. J Differ Equ, 1999,
153: 225–291

[13] Liu T -P, Zeng, Y. Time-asymptotic behavior of wave propagation around a viscous shock profile. Comm
Math Phys, 2009, 290(1): 23–82

[14] Liu T -P, Zeng Y. Shock waves in conservation laws with physical viscosity. Preprint

[15] MacCamy R C. A model for one-dimensional nonlinear viscoelasticity. Quart Appl Math, 1977, 35: 21–33

[16] Markowich P, Renardy M. Lax-Wendroff methods for hyperbolic history value problems. SIAM J Numer Anal, 1984, 21: 24–51; Errata, 1985, 22: 204

[17] Shu C -W, Zeng Y. High-order essentially non-oscillatory scheme for viscoelasticity with fading memory.
Quart Appl Math, 1997, 55(3): 459–484

[18] Sta?ans O. On a nonlinear hyperbolic Volterra equation. SIAM J Math Anal, 1980, 11: 793–812

[19] Yong W -A. Entropy and global existence for hyperbolic balance laws. Arch Ration Mech Anal, 2004, 172(2): 247–266

[20] Zeng Y. Convergence to di?usion waves of solutions to nonlinear viscoelastic model with fading memory.
Commun Math Phys, 1992, 146: 585–609

[21] Zeng Y. L asymptotic behavior of compressible, isentropic, viscous 1-D flow. Comm Pure Appl Math,
1994, 47(8): 1053–1082

[22] Zeng Y. L asymptotic behavior of solutions to hyperbolic-parabolic systems of conservation laws. Arch
Math (Basel), 1996, 66: 310–319

[23] Zeng Y. Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation. Arch
Rational Mech Anal, 1999, 150(3): 225–279

[24] Zeng Y. Gas flows with several thermal nonequilibrium modes. Arch Rational Mech Anal, 2010, 196:
191–225