Publication Cover
Applicable Analysis
An International Journal
Volume 67, 1997 - Issue 3-4
36
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Existence of global weak solutions for a viscoelastic model with relaxation

, &
Pages 313-326 | Received 01 Aug 1997, Published online: 02 Nov 2010

References

  • Ball , J.M. 1977 . Convexity conditons and existence theorems in the nonlinear elasticity . Arch. Rational Mech. Anal , 63 : 337 – 403 .
  • Chen , G.Q. and Liu , T.P. 1993 . Zero relaxation and dissipation limits for hyperbolic conservation laws . Comm. Pure Appl. Math , 46 : 755 – 781 .
  • Ding , X.X. , Chen , G.Q. and Luo , P.Z. 1985 . Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics I., II . Acta Math. Sci , 5 : 415,433 – 432,472 .
  • DiPerna , R.J. 1983 . Convergence of approximate solutions to conservation laws . Arch. Rational Mech. Anal , 82 : 27 – 70 .
  • Greenberg , J.M. and Hsiao , L. 1983 . The Riemannn problem for system . Arch. Rational Mech. Anal , 82 : 87 – 108 .
  • Lax , P.D. 1971 . “ Shock waves and entropy ” . In In Contributions to Nonlinear Functional Analysis , Edited by: Zarantonello , E.A. 603 – 634 . Academic Press .
  • Lin , P.X. 1992 . Young measures and an application of compensated compactness to onedimensional nonlinear elastodynamics . Trans. Amer. Math. Soc , 329 : 377 – 413 .
  • Liu , T.P. 1987 . Hyperbolic conservation laws with relaxation . Comm. Math. Phys , 108 : 153 – 175 .
  • Murat , F. 1981 . L'injection du cone positif de H-1 dans W-1,q est compacte pour tout q<2 . J. Math. Pures Appl , 60 : 309 – 322 .
  • Schonbek , M.E. 1982 . Convergence of solutions to nonlinear dispersive equations . Comm. Partial Diff. Equs , 7 : 959 – 1000 .
  • Serre , D. 1986 . La compacité par compensation pour les systems hyperboliques non linéaires de deux equations à une dimensions d'espace . J. Math. Pures Appl , 65 : 423 – 468 .
  • Tartar , L. 1979 . “ Compensated compactness and applications to partial differential equations, In Nonlinear Analysis and Mechanics ” . In Heriot-Watt Symposium, IV Edited by: Knops , R.J. 136 – 192 . Harlow, Longman Pitman Research Notes in Mathematics
  • Yang , T. , Zhu , C.J. and Zhao , H.J. 1997 . Compactness Framework of Lp approximate solutions for scalar conservation laws . Preprint
  • Zhao , H.J. 1996 . Existence and uniquencess of the global admissible solution for a viscoelastic model with relaxation . Proc. Royal Soc. Edin , 126A : 1113 – 1132 .
  • Zhu , C.J. 1995 . Global resolvability for a viscoelastic model with relaxation, . Proc. Royal Soc. Edin. , 125A : 1277 – 1285 .
  • Zhu , C.J. 1994 . Existence and uniqueness of the entropy solution for a viscoelastic model . Preprint

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.