M. Nedeljkov
Delta and Singular Delta Locus for One Dimensional Systems of Conservation Laws
Preprint series: ESI preprints

MSC:

35L65 Conservation laws

35L67 Shocks and singularities, See also {58C27, 76L05}

35D05 Existence of generalized solutions

Abstract: A condition for existence of singular and delta shock waves for
systems of conservation laws is given in the paper. The systems considered
here have fluxes which are linear in one of the dependent variables.
The condition obtained here is analogous to the one for the standard
Hugoniot locus. Three different solution concept are used in the paper:
associated solution in Colombeau sense,
limits of nets of smooth functions together with Rankin-Hugoniot
conditions and a kind of a measure valued solutions.


Keywords: conservation laws, generalized solutions, delta shock waves, singular shock waves, Colombeau algebra of generalized functions