Delta and Singular Delta Locus for One Dimensional Systems of Conservation Laws
نویسندگان
چکیده
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.
منابع مشابه
DELTA AND SINGULAR DELTA LOCUS FOR ONEDIMENSIONAL SYSTEMS OF CONSERVATION LAWSMarko
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 uxes which are linear in one of the dependent variables. The condition obtained here is analogous to the one for the standard Hugoniot locus. Three diierent solution concept are used in the paper: associated solution in Colombeau sense, limits of n...
متن کاملSingular Solutions for Nonlinear Hyperbolic Systems
An extension of the method of weak asymptotics is presented which allows the construction of singular solutions of Riemann problems for systems of hyperbolic conservation laws. The method is based on using complex-valued approximations which become real-valued in the distributional limit. It is shown how this approach can be used to construct solutions containing combinations of classical hyper...
متن کاملδ-Shock wave as a new type solutions of hyperbolic systems of conservation laws
A concept of a new type of singular solutions to hyperbolic systems of conservation laws is introduced. It is so-called δ-shock wave, where δ is n-th derivative of the delta function. We introduce a definition of δ′-shock wave type solution for the system ut + ( f(u) ) x = 0, vt + ( f ′(u)v ) x = 0, wt + ( f ′′(u)v2 + f ′(u)w ) x = 0. Within the framework of this definition, the Rankine–Hugonio...
متن کاملSelf-similar solutions of the Riemann problem for two-dimensional systems of conservation laws
In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem
متن کاملOn the Delta-shock Front Problem
In this paper the δ-shock front problem is studied. For some classes of hyperbolic systems of conservation laws (in several space dimension, too) we introduce the definitions of a δ-shock wave type solution relevant to the front problem. The Rankine–Hugoniot conditions for δ-shocks are analyzed from both geometrical and physical points of view. δ-Shock balance relations connected with area and ...
متن کامل