Abstract:The problem of definingδ-shock wave type solutionsof hyperbolic systems of conservation laws in connection with the constructingsingular superpositionsproducts of distributions is studied. We illustrate this problem by constructing δ-shock wave type solutions for two systems. One of them,uis a generalization of the well-known Keyfitz--Kranzer system, where_{t}+ (f(u)-v)_{x}=0, v_{t}+ g(u)_{x}=0,f(u)andg(u)are polynomials of degreenandn+1, respectively,nis an even integer. The other one is the systemuwhere_{t}+f(u)_{x}=0, v_{t}+(vg(u))_{x}=0,f(u),g(u)are smooth functions. As far as we know, exact-shock wave type solutions for the first system have never been constructed.

**Paper:**- Available as PDF (256 Kbytes), Postscript (480 Kbytes) or gzipped PostScript (216 Kbytes; uncompress using gunzip).
**Author(s):**- V. M. Shelkovich, <shelkv@VS1567.spb.edu>
**Publishing information:**- Revised version October 23 2004.
**Comments:****Submitted by:**- <shelkv@VS1567.spb.edu> October 20 2004.

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