We consider front tracking approximate solutions to the p-system of isentropic gas dynamics. At interaction times, the outgoing wave fronts have the same strength as in the exact solution of the Riemann problem, but some error is allowed in their speed. For large BV initial data, we construct examples showing that the total variation of these approximate solutions can become arbitrarily large, ...

We prove that isentropic gas flow does not admit non-degenerate TVD fields on any invariant set M(r0, s0) = {r0 < r < s < s0}, where r, s are Riemann coordinates. A TVD field refers to a scalar field whose spatial variation VarX(φ(τ(t,X), u(t,X))) is nonincreasing in time along entropic solutions. The result is established under the assumption that the Riemann problem defined by an overtaking s...

The one–dimensional differential equations for the conservation mixture mass and mixture momentum coupled by a relative velocity conservation equation have been solved for an isentropic mixture of gas and liquid two–phase flow. Under certain restrictions the resulting system of partial differential equations is hyperbolic and allow discontinuous solutions. These equations have been solved by th...

This paper deals with conservation laws on networks, represented by graphs. Entropy-type conditions are considered to determine dynamics at nodes. Since entropy dispersion is a local concept, we consider a network composed by a single node J with n incoming and m outgoing arcs. We extend at J the classical Kružkov entropy obtaining two conditions, denoted by (E1) and (E2): the first requiring e...

We study the Cauchy problem for the Aw-Rascle-Zhang model for traffic flow with a flux constraint at x = 0. More precisely we consider the Riemann solver, conserving the number of cars at x = 0 but not the generalized momentum, introduced in [9] for the problem with flux constrained. For such a Riemann solver, we prove existence of a solution for the Cauchy problem. The proof is based on the wa...

A direct Eulerian generalized Riemann problem (GRP) scheme is derived for compressible fluid flows. Riemann invariants are introduced as the main ingredient to resolve the generalized Riemann problem (GRP) directly for the Eulerian formulation. The crucial auxiliary Lagrangian scheme in the original GRP scheme is not necessary in the present framework. The delicate sonic cases can be easily tre...

Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis. For any given initial data with two pieces of constant states, the Riemann solutions are constructed as a combination of elementary waves. When the initial profile contains three pieces of constant states, the solution may be constructed from the Riemann solutions, with each two adjacen...

We investigate viscous shock profiles of the Riemann problem for systems of hyperbolic balance laws. Even strictly hyperbolic flux terms together with a nonoscillating kinetic part can lead to oscillating viscous shock profiles. They appear near a Hopf-like bifurcation point of the traveling wave equation.

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in [32, 7, 6]. Recently, it has been observed in [3] that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in [7], based on the high order finite volume WENO scheme with subcell resolution and utilizing...

A strategy for proving Riemann hypothesis is suggested. The vanishing of the Rieman Zeta reduces to an orthogonality condition for the eigenfunctions of a non-Hermitian operator D+ having the zeros of Riemann Zeta as its eigenvalues. The construction of D+ is inspired by the conviction that Riemann Zeta is associated with a physical system allowing conformal transformations as its symmetries. T...