The inverse scattering problem on half-axis, in other words, in the spherically symmetric case, consists of finding the unknown potential from a suitable class from the scattering data S. The other problem of practical interest is to find this potential from the spectral data dρ(λ). In the literature there are recovery procedures for finding the potential from the spectral or from the scatterin...

In this paper we first briefly review the semi-analytical method [20] for solving the Derivative Riemann Problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection...

Consider a junction with n incoming and m outgoing roads. Along each road, the flow of traffic is described through the continuum model displaying phase transitions introduced in [5]. This note provides a Riemann solver for the resulting Riemann problem at the junction. 2000 Mathematics Subject Classification: 35L65, 90B10.

We prove that any quasirandom dense large graph in which all degrees are equal and even can be decomposed into given collection of two-factors (2-regular spanning subgraphs). A special case this result gives a new solution to the Oberwolfach problem.

We present a domain-theoretic analysis of the invariant measure of the one-dimensional Ising model in a random external magnetic eld. The invariant measure is obtained as a xed point of the Markov transition operator of an iterated function system with probabilities acting on the probabilistic power domain of the upper space of a closed real interval. This enables us to use the generalised Riem...

This paper studies many fundamental aspects of a newly proposed multi-class traffic flow model. For the first time it presents a complete discussion on the hyperbolicity of the system; and based upon this, the admissible waves of the Riemann problem are deeply investigated. Many important conclusions are made in discussions, and the related physical meanings are interpreted. For the confirmatio...

We consider the complete Euler system describing the time evolution of an inviscid nonisothermal gas. We show that the rarefaction wave solutions of the 1D Riemann problem are stable, in particular unique, in the class of all bounded weak solutions to the associated multiD problem. This may be seen as a counterpart of the non-uniqueness results of physically admissible solutions emanating from ...

We analize the structure of the general solution of the Riemann problem for a striclty hyperbolic system of conservation laws whose characteristic elds are neither genuinely non-linear nor linearly degenerate in the sense of Lax.

where p(t, z), ~(2, t) are the mean density and velocity of the flow, p(z, t) is the pressure. Assume the gas under consideration is polytropic. Then the temperature, density, and pressure are related with RT = p/p where R is a positive constant proportional to the molecular weight of gas and assumed to be unit for simplicity. So p = Tp. Roughly speaking, the pressure p vanishes as T goes to ze...