Zero Relaxation Limit for Piecewise Smooth Solutions to a Rate-Type Viscoelastic System in the Presence of Shocks

✍ Scribed by Hailiang Li; Ronghua Pan

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 171 KB
• Volume: 252
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7005

✦ Synopsis

We study a rate-type viscoelastic system proposed in I. Suliciu Int. J. Engng. Ž . . Sci. 28 1990 , 827᎐841 , which is a 3 = 3 hyperbolic system with relaxation. As the relaxation time tends to zero, this system converges to the well-known p-system formally. In 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 Ž matched asymptotic analysis suggested in J. Goodman and Z. P. Xin Arch. Ration. Ž . . Mech. Anal. 121 1992 , 235᎐265 , which includes two parts: the matched asymptotic expansion and stability analysis.