Construction of Riemann solutions for a hyperbolic system in conservative form arising from
the one-dimensional mean-field games with the quadratic Hamiltonian and the logarithmic …

Two kinds of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the
logarithmic equation of state are explicitly obtained by using the combination between 1 …

The Brio system is a two-by-two system of conservation laws arising as a simplified model in
ideal magnetohydrodynamics (MHD). The system has the form\begin {align*}\partial_t …

The present paper concerns the system ut+[ϕ (u)] x= 0, vt+[ψ (u) v] x= 0 having distributions
as initial conditions. Under certain conditions, and supposing ϕ, ψ: ℝ→ ℝ functions, we …

A weak notion of solution for systems of conservation laws in one dimension is put forward.
In the framework introduced here, it can be shown that the Cauchy problem for any n× n …

In this work, we study the system of conservation laws that is strictly hyperbolic and whose
Riemann solution contains delta shock waves as well as classical elementary waves. In …

This paper studies a Riemann problem for the isentropic Euler equations and addresses two
gaps in the literature concerning positive pressures. Such study is made using a product of …

We study the vanishing viscosity limit of a non-strictly hyperbolic system of balance laws
known as the 1D Saint-Venant model whose solution admits δ-waves. The balance term …

Modelling of wave motion in a fluid is usually based on classical systems which are obtained
by the hypotheses that the flow is irrotational and the bottom is even. In such a context, the …