Related papers: The particle paths of hyperbolic conservation laws
We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric…
This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…
This paper is concerned with the large time behaviors of the entropy solutions to one-dimensional scalar convex conservation laws, of which the initial data are assumed to approach two arbitrary $ L^\infty $ periodic functions as $…
In paper [S.I. Senashov, A. Yakhno. 2012. SIGMA. Vol.8. 071] the variant of the hodograph method based on the conservation laws for two hyperbolic quasilinear equations of the first order is described. Using these results we propose a…
We prove the H\"older regularity of continuous isentropic solutions to multi-dimensional scalar balance laws when the source term is bounded and the flux satisfies general assumptions of nonlinearity. The results are achieved by exploiting…
We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $\rho$ ahead. The averaging kernel is of exponential type: $w_\varepsilon(s)=\varepsilon^{-1}…
Hydrodynamic transport coefficients may be evaluated from first principles in a weakly coupled scalar field theory at arbitrary temperature. In a theory with cubic and quartic interactions, the infinite class of diagrams which contribute to…
The aim of this article is to study the limiting behavior of the solutions for the scaled generalized Euler equations of compressible fluid flow. When the initial data is of Riemann type, we showed the existence of solution which consists…
We consider two scalar conservation laws with non-local flux functions, describing traffic flow on roads with rough conditions. In the first model, the velocity of the car depends on an averaged downstream density, while in the second model…
In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
In this paper, we study the initial value problem of a Boltzmann type equation with a nonlinear degenerate damping. We prove the existence of global weak solutions with large initial data, in three dimensional space. We rely on a variant…
In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes…
Solutions to a class of conservation laws with discontinuous flux are constructed relying on the Crandall-Liggett theory of nonlinear contractive semigroups~\cite{CL}. In particular, the paper studies the existence of backward Euler…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
It is shown that the steady unidirectional flow with vanishing heat flux considered by B. C. Eu [Phys. Rev. E 65, 031202 (2002)], and earlier by Uribe and Garcia--Colin [Phys. Rev. E 60, 4052 (1999)], is inconsistent with the exact…
We propose a new sufficient non-degeneracy condition for the strong precompactness of bounded sequences satisfying the nonlinear first-order differential constraints. This result is applied to establish the decay property for periodic…
A complex integral formula provides an explicit solution of the initial value problem for the nonlinear scala 1D equation $u_t+[f(u)]_x = 0$, for any flux $f(u)$ and initial condition $u_0(x)$ that are analytic. This formula is valid at…
The kinematic wave model of traffic flow on a road network is a system of hyperbolic conservation laws, for which the Riemann solver is of physical, analytical, and numerical importance. In this paper, we present a Riemann solver at a…
Nonlinear conservation laws subject to random initial conditions pose fundamental problems in the evolution and interactions of shocks and rarefactions. Using a discrete set of values for the solution, we derive a hierarchy of equations in…