Zero relaxation limit for piecewise smooth solutions to a rate-type viscoelastic system in the presence of shocks

[摘要] We study a rate-type viscoelastic system proposed in I. Suliciu (Int. J. Engng. Sci. 28 (1990), 827-841), which is a 3 x 3 hyperbolic system with relaxation. As the relaxation time tends to zero, this system converges to the well-known p-system formally. Zn the case that the solutions of the p-system are piecewise smooth, including finitely many noninteracting shock waves, we show that there exist smooth solutions for Suliciu's model which converge to those of the p-system strongly as the relaxation time goes to zero. The method used here is the so-called matched asymptotic analysis suggested in J. Goodman and Z. P. Xin (Arch. Ration. Mech. Anal. 121 (1992), 235-265), which includes two parts: the matched asymptotic expansion and stability analysis. (C) 2000 Academic Press.

[发布日期] 2000-12-01

[关键词] piecewise smooth solution;viscoelasticity;matched asymptotic analysis;zero relaxation limit