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Volume 10, Issue 4
Global Solutions in L^infinity for a System of Conservation Laws of Viscoelastic Materials with Memory

Gui-Qiang Chen & M. Dafermos Constantine

J. Part. Diff. Eq., 10 (1997), pp. 369-383.

Published online: 1997-10

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  • Abstract
We construct global solutions in L^∞ for the equations of motion or one-dimensional viscoelastic media, in Lagrangian coordinates, with arbitrarily large L^∞ initial data, via the vanishing viscosity method. A priori estimates for approximate solutions, with artificial viscosity, are derived through entropy inequalities. The convergence of the approximate solutions to a weak solution compatible with the entropy condition is demonstrated. This also establishes the compactness of the corresponding solution operators, which indicates that the memory effect does not affect the hyperbolic behavior.
  • Keywords

Viscosity method viscoelasticity global solutions convergence solution operators

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COPYRIGHT: © Global Science Press

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@Article{JPDE-10-369, author = {Gui-Qiang Chen and M. Dafermos Constantine }, title = {Global Solutions in L^infinity for a System of Conservation Laws of Viscoelastic Materials with Memory}, journal = {Journal of Partial Differential Equations}, year = {1997}, volume = {10}, number = {4}, pages = {369--383}, abstract = { We construct global solutions in L^∞ for the equations of motion or one-dimensional viscoelastic media, in Lagrangian coordinates, with arbitrarily large L^∞ initial data, via the vanishing viscosity method. A priori estimates for approximate solutions, with artificial viscosity, are derived through entropy inequalities. The convergence of the approximate solutions to a weak solution compatible with the entropy condition is demonstrated. This also establishes the compactness of the corresponding solution operators, which indicates that the memory effect does not affect the hyperbolic behavior.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5606.html} }
TY - JOUR T1 - Global Solutions in L^infinity for a System of Conservation Laws of Viscoelastic Materials with Memory AU - Gui-Qiang Chen & M. Dafermos Constantine JO - Journal of Partial Differential Equations VL - 4 SP - 369 EP - 383 PY - 1997 DA - 1997/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5606.html KW - Viscosity method KW - viscoelasticity KW - global solutions KW - convergence KW - solution operators AB - We construct global solutions in L^∞ for the equations of motion or one-dimensional viscoelastic media, in Lagrangian coordinates, with arbitrarily large L^∞ initial data, via the vanishing viscosity method. A priori estimates for approximate solutions, with artificial viscosity, are derived through entropy inequalities. The convergence of the approximate solutions to a weak solution compatible with the entropy condition is demonstrated. This also establishes the compactness of the corresponding solution operators, which indicates that the memory effect does not affect the hyperbolic behavior.
Gui-Qiang Chen and M. Dafermos Constantine . (1997). Global Solutions in L^infinity for a System of Conservation Laws of Viscoelastic Materials with Memory. Journal of Partial Differential Equations. 10 (4). 369-383. doi:
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