In a previous paper (Transp. Porous Media, 55(1): 47–70), algorithms are given for computing the analytical solution to the three-phase Riemann problem. Application of those algorithms requires that the wave configuration is known. The purpose of this note is to provide a procedure to determine the wave structure for any initial and injected saturation states.

In this paper we discuss the role of curvature in the context of color spaces. Curvature is a differential geometric property of color spaces that has attracted less attention than other properties like the metric or geodesics. In this paper we argue that the curvature of a color space is important since curvature properties are essential in the construction of color coordinate systems. Only co...

We consider the Riemann problem for non-genuinely nonlinear conservation laws where the flux function admits two inflection points. This is a simplification of van der Waals fluid pressure, which can be seen as a function of the specific volume for a specific entropy at which the system lacks the non-genuine nonlinearity. Corresponding to each inflection point, A nonclassical Riemann solver can...

An extension of the Colombo phase transition model is proposed. The congestion phase is described by a two-dimensional zone defined around an equilibrium flux known as the classical fundamental diagram. General criteria to build such a set-valued fundamental diagram are enumerated, and instantiated on several equilibrium fluxes with different concavity properties. The solution of the Riemann pr...

Abstract. In this paper, we investigate a traffic model similar to the Lighthill–Whitham– Richards model, consisting of a hyperbolic conservation law with a discontinuous, non-convex, piecewise-linear flux. Using Dias and Figueira’s mollification framework, analytical solutions to the corresponding Riemann problem are derived. For certain initial data, these Riemann problems can generate zero w...

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

In this article, we obtain generalizations for Grüss type integral inequality by using h(x)-Riemann-Liouville fractional integral.

We aim to introduce extended generalized Mittag-Leffler function (EGMLF) via the Beta and obtain certain integral differential representation of them. Further, we present some formulas Riemann-–Liouville fractional integration differentiation operators. Also, derive various transforms, including Euler transform, Laplace Whittakar transform K-transform. The operator images are expressed in terms...

An approximate Riemann solver for the equations of ideal relativistic magnetohydrodynamics is presented. The solver belongs to the so-called Harten-Laxvan Leer (HLL, [1]) family of solvers where an initial guess to the characteristic wave speeds is given without any knowledge a priori of the solution. Our proposed method of solution generalizes to the relativistic case the classical five-wave H...

In this paper we present the exact solution of the Riemann Problem for the non-linear shallow water equations with a step-like bottom. The solution has been obtained by solving an enlarged system obtained by adding an additional equation for the bottom geometry and then using the principles of conservation of mass and momentum across the step. The resulting solution is unique and satis es the p...