Conservation laws, delta-shocks and singular shocks. (English) Zbl 0933.35134

Keyfitz, Barbara Lee

Grosser, Michael (ed.) et al., Nonlinear theory of generalized functions. Proceedings of the workshop on nonlinear theory of nonlinear functions, Erwin-Schrödinger-Institute, Vienna, Austria, October–December 1997. Boca Raton, FL: Chapman & Hall. Chapman Hall/CRC Res. Notes Math. 401, 99-111 (1999).

The paper is a survey of investigations of model conservation law systems, that have no classical solution. The author also formulates open problems concerning the existence of weak solutions of the system in the large, conditions under which there exist singular shocks and sensibility of a system on nonlinear transformations.
For the entire collection see [Zbl 0918.00026].

Reviewer: Marie Kopáčková (Praha)

MSC:

35L67	Shocks and singularities for hyperbolic equations
35B65	Smoothness and regularity of solutions to PDEs
35L65	Hyperbolic conservation laws

Keywords:

no classical solution; double characteristic