Abstract:We construct $\delta$-shock wave type solutions of the Cauchy problem for the system of conservation lawsuwhere $f(u)$ and $g(u)$ are polynomials of degree $n$ and $n+1$, respectively, $n$ is even. A well known particular case of this system was studied in~\cite{KeKr},~\cite{KrKe} by B.~L.~Keyfitz and H.~C.~Kranzer. In this paper a techniques of the {\it weak asymptotics method} and the definition of a $\delta$-shock type solution introduced by V.~G.~Danilov and V.~M.~Shelkovich~\cite{DS3}--~\cite{DS5}, are used._{t}+(f(u)-v)_{x}=0, v_{t}+g(u)_{x}=0,Geometric and physics sense of the Rankine--Hugoniot conditions for $\delta$-shocks is given for the above system, for the system

uand for the well-known zero-pressure gas dynamics system. The geometric aspect of $\delta$-shock wave formation from sufficiently smooth compactly supported initial data is considered. Namely, the construction for the position of $\delta$-shock in a breaking wave is given._{t}+f(u)_{x}=0, v_{t}+(g(u)v)_{x}=0,

**Paper:**- Available as PDF (304 Kbytes) or gzipped PostScript (224 Kbytes; uncompress using gunzip).
**Author(s):**- V. M. Shelkovich, <shelkv@svm.abu.spb.ru>
**Publishing information:****Comments:**- Revised version submitted on December 2 2003.
**Submitted by:**- <shelkv@svm.abu.spb.ru> September 16 2003.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | All Preprints | Preprint Server Homepage ]

Conservation Laws Preprint Server <conservation@math.ntnu.no> Last modified: Tue Dec 2 08:52:05 MET 2003