Algebraic aspects of multidimensional δ-shocks and singularities of flux-functions

The algebraic aspects of δ-shock wave type solutions to multidimensional systems of conservation laws are studied. We show that any singular solution of the Cauchy problem generates some algebraic relations between its distributional components (“right” singular superpositions of distributions). We prove that the nonlinear flux-functions for δ-shock solutions are well defined Schwartz distributions, and describe their singularities.