Preprint 1998-001

Singular Perturbations of First-Order Hyperbolic Systems with Stiff Source Terms

Wen-An Yong


Abstract:

This work develops a singular perturbation theory for initial-value problems of nonlinear first-order hyperbolic systems with stiff source terms in several space variables. It is observed that under reasonable assumptions, many equations of classical physics of that type admit a {\sl structural stability condition}. This condition is equivalent to the well-known subcharacteristic condition for one-dimensional $2\times 2$-systems and the well-known time-like condition for scalar second-order hyperbolic equations with a small positive parameter multiplying the highest derivatives. Under this stability condition, we construct a formal asymptotic expansion for the solution to the nonlinear problems. Furthermore, assuming some regularity of the solutions to the limiting inner problems and the reduced problems, we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal expansion.

The stability condition seems to be a key to the problems of this kind and can be easily verified. Moreover, this presentation unifies and improves earlier works for some specific equations.



Paper:
Available as PostScript
Title:
Singular perturbations of first-order hyperbolic systems with stiff source terms
Author(s):
Wen-An Yong, mailto:yong@utopie.iwr.uni-heidelberg.de
Publishing information:
Comments:
Submitted by:
mailto:yong@utopie.iwr.uni-heidelberg.de January 15 1998.


[ 1996 Preprints | 1997 Preprints | 1998 Preprints | All Preprints | Preprint Server Homepage ]
(c) The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

mailto:conservation@math.ntnu.no
Last modified: Thu Jan 15 15:40:55 1998
Сайт управляется системой uCoz