Related papers: Transport and concentration processes in the multi…
{\it $\delta$-Shock wave type solutions} in the multidimensional system of conservation laws $$ \rho_t + \nabla\cdot(\rho F(U))=0, \qquad (\rho U)_t + \nabla\cdot(\rho N(U))=0, \quad x\in \bR^n, $$ are studied, where $F=(F_j)$ is a given…
In this paper, firstly, by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation, we construct parameterized delta-shock and constant density solutions, then we show that, as the flux perturbation…
The relativistic full Euler equations for a Chaplygin gas are studied. The Riemann problem is solved constructively. There are two kinds of Riemann solutions, in which one consists of three contact discontinuities and the other involves a…
By using the Hamilton principle of stationary action, we derive the governing equations and Rankine-Hugoniot conditions for continuous media where the specific energy depends on the space and time density derivatives. The governing system…
As a shock wave propagates through a gas mixture, pressure, temperature, and density increase across the shock front. Rankine-Hugoniot (R-H) relations quantify these changes, correlating post-shock quantities with upstream conditions…
In this paper, we investigate the formation and propagation of singularities for the system for one-dimensional Chaplygin gas, which is described by a quasilinear hyperbolic system with linearly degenerate characteristic fields. The…
In this article, we investigate the two-dimensional pressureless Euler equations with three constant Riemann initial data. Our primary focus is on the wave interactions involving contact discontinuities and delta shocks. A distinguishing…
We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyse the retarded two point functions involving the charge and the associated currents at long wavelengths,…
In this paper, the Riemann problem for the pressureless Euler equations with a discontinuous source term is considered. The delta shock wave solution is obtained by combining the generalized Rankine-Hugoniot conditions together with the…
The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…
The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and non-equilibrium thermodynamics. The governing equations of irreversible…
In this paper we discuss delta shock interaction problem for a pressureless gas dynamics system with two different ways of approaching the subject. The first one is by using shadow wave solution concept. The result of two delta shock…
Similarity solutions are obtained for one dimensional, unsteady, adiabatic propagation of an exponential shock wave in a perfect gas with heat conduction and radiation heat flux, in the presence of azimuthal magnetic field. The shock wave…
We present a self-similar solution to describe the propagation of a shock wave whose energy is deposited or lost at the front. Both of the propagation of the shock wave in a medium having a power-law density profile and the expansion of the…
A systematic procedure to derive shell models for MHD turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross-helicity and the magnetic helicity as well as the…
We consider heat transport through systems with broken time-reversal symmetry. We apply strong magnetic fields to weakly charged particle systems, where the dynamics are dominated by the Lorentz force and spring forces. The standard…
We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…
Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…