Preprint 2000-012

Life-span of classical solutions to quasilinear hyperbolic systems with slow decay initial data

De-xing Kong

Abstract: In this paper the author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with ``slow'' decay initial data. By constructing an example, the author first illustrates that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. The author then gives some lower bounds of the life-span of classical solutions in the case that system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, the author proves that Theorems 1.1 and 1.2 in [2] are still valid for this kind of initial data.

Available as PostScript (367 Kbytes).
De-xing Kong, <>
Publishing information:
An earlier version of this paper was available from these archives as preprint 1999-016.
Submitted by:
<> April 18 2000.

[ 1996 | 1997 | 1998 | 1999 | 2000 | All Preprints | Preprint Server Homepage ]
© 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.

Conservation Laws Preprint Server <>
Last modified: Wed Mar 22 09:02:18 2000