Advanced Search

We discuss the definitions of singular solutions (in the form of integral identities) to systems of conservation laws such as shocks, δ-, δ’-, and ${\delta }^{\left(n\right)}$-shocks (n = 2,3,...). Using these definitions, the Rankine-Hugoniot conditions for δ- and δ’-shocks are derived. The weak asymptotics method for the solution of the Cauchy problems admitting δ- and δ’-shocks is briefly described. The algebraic aspects of such singular solutions are studied. Namely, explicit formulas for flux-functions of singular solutions...