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Applicable Analysis
An International Journal
Volume 77, 2001 - Issue 3-4
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Original Articles

Global existence and formation of singularities in thermoviscoelasticity of integral typeFootnote

Singularities in thermoviscoelasticity of integral type

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Pages 273-296 | Received 01 Feb 2000, Published online: 02 May 2007

References

  • Alikakos , N.D. 1979 . An application of the invariance principle to reaction-diffusion equations . J. Diff. Equations , 33 : 201 – 225 .
  • Dafermos , C. M. 1982 . Global smooth solutions to the initial boundary value for the equations of one-dimensional nonlinear thermoviscoelasticity . SIAM J, Math. Anal , 13 : 397 – 408 .
  • Dafermos , C. M. 1986 . Development of singularities in the motion of materials with fading memory . Arch. Rat. Mech. Anal , 91 : 193 – 205 .
  • Dafermos , C. M. and Hsiao , L. 1982 . Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity . Nonlinear Anal. T.M.A , 6 : 435 – 454 .
  • Dafermos , C M. and Hsiao , L. 1986 . Development of singularities in solutions of the equations of nonlinear thermoelasticity . Quart. Appl. Math , 44 : 463 – 474 .
  • Gurtin , M.E. and Hrusa , W.J. 1991 . On the thermodynamics of viscoelastie materials of single- integral type . Quart. Appl. Math , XLIX : 68 – 85 .
  • Hrusa , W.J. and Messaoudi , S.A. 1990 . On formation of singularities in one dimensional nonlinear thermoelasticity . Arch. Rat. Mech. Anal , 111 : 135 – 151 .
  • Jiang , S. 1993 . Global large solutions to initial boundary value problems in one-dimensional non- linear thermoviscoelasticity . Quart. Appl. Math , 51 : 731 – 744 .
  • Kawashima , S. . Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnethohydrodynamics . Thesis . 1983 . Kyoto Univ .
  • Nohel , J.A. and Renardy , M. “ Development of singularities in nonlinear viscoelasticity ” . In In: Amorphous Polymers and Non-Newtonian Fluids, IMA Volumes in Math , Vol. 6 , Springer- Verlag .
  • Racke , R. 1992 . Mathematical Aspects in Nonlinear Thermoelasticity , Universität Bonn . SFB 256 Vorlesungsreihe No. 25
  • Racke , R. and Shibata , Y. 1991 . Global smooth solution and asymptotic stability in one dimensional nonlinear thermoelasticity . Arch. Rat. Mech. Anal , 116 : 1 – 34 .
  • Racke , R. , Shibata , Y. and Zheng , S. 1993 . Global solvability and exponential stability in one dimensional nonlinear thermoelasticity . Quart. Appl, Math , 51 : 751 – 763 .
  • Renardy , M. , Hrusa , W.J. and Nohel , J.A. 1987 . Mathematical Problems in Viscoelasticity , New York : John Wiley .
  • Slemrod , M. 1981 . Global existence, uniqueness and asymptotic stability of classical smooth solutions in one-dimensional non-linear thermoelasticity . Arch. Rat. Mech. Anal , 76 : 97 – 133 .

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