Delta-shock Wave Type Solution of Hyperbolic Systems of Conservation Laws
نویسندگان
چکیده
For some classes of hyperbolic systems of conservation laws we introduce a new definition of a δ-shock wave type solution. This definition gives natural generalizations of the classical definition of the weak solutions. It is relevant to the notion of δ-shocks. The weak asymptotics method developed by the authors is used to describe the propagation of δ-shock waves.
منابع مشابه
δ-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 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 کاملDelta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type
This paper is devoted to the study of delta shockwaves for a hyperbolic systemof conservation laws of Keyfitz-Kranzer typewith two linearly degenerate characteristics.TheRiemannproblem is solved constructively.TheRiemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-...
متن کاملDelta Shock Wave Formation in the Case of Triangular Hyperbolic System of Conservation Laws
We describe δ shock wave arising from continuous initial data in the case of triangular conservation law system arising from ”generalized pressureless gas dynamics model” (e.g. [12]). We use the weak asymptotic method [8, 9]. In this paper we investigate formation of δ-shock wave in the case of triangular system of conservation laws: ut + (f(u))x = 0, (1) vt + (vg(u))x = 0, (2) with continuous ...
متن کاملThe comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws
This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...
متن کامل