TY - JOUR
T1 - Global Solutions in <em>L</em>^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.