Related papers: Scalar conservation laws with multiple rough fluxe…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…
This paper is concerned with the stability of stationary solutions of the conservation law $\partial_t u + \mathrm{div}_y A(y,u) -\Delta_y u=0$, where the flux $A$ is periodic with respect to its first variable. Essentially two kinds of…
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative,…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
In this paper, we established a quadratic transportation cost inequality for scalar stochastic conservation laws driven by multiplicative noise. The doubling variables method plays an important role.
Derivation of governing equations for multiphase flow on the base of thermodynamically compatible systems theory is presented. The mixture is considered as a continuum in which the multiphase character of the flow is taken into account. The…
In this paper, we first investigate quasi-entropy solutions to scalar conservation laws in several space dimensions. In this setting, we introduce a suitable Lagrangian representation for such solutions. Next, we prove that, in one space…
In this paper, we establish a small time large deviation principles for scalar stochastic conservation laws driven by multiplicative noise. The doubling of variables method plays a key role.
We prove the convergence of the explicit-in-time Finite Volume method with monotone fluxes for the approximation of scalar first-order conservation laws with multiplicative, compactly supported noise.
We are interested in 2x2 systems of conservation laws of special structure, including generalized Aw-Rascle and Zhang (GARZ) models for road traffic. The simplest representative is the Keyfitz-Kranzer system, where one equation is nonlinear…
We focus on entropy admissible solutions of scalar conservation laws in one space dimension and establish new regularity results with respect to time. First, we assume that the flux function $f$ is strictly convex and show that, for every $…
We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function $a$ is strictly…
We establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function $f(k(x,t),u)$, where the coefficient $k(x,t$ is $BV$-regular and may exhibit…
In this paper, we discuss the asymptotic behaviour of weak solutions to the Cauchy problem toward the viscous shock waves for the scalar viscous conservation law. We firstly consider the case that the flux function is the quadratic Burgers…
Two aspects of a widely used 1D model of blood flow in a single blood vessel are studied by symmetry analysis, where the variables in the model are the blood pressure and the cross-section area of the blood vessel. As one main result, all…
The Enskog kinetic theory of multicomponent granular suspensions employed previously [G\'omez Gonz\'alez, Khalil, and Garz\'o, Phys. Rev. E \textbf{101}, 012904 (2020)] is considered further to determine the four transport coefficients…
Conserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in $n>1$ dimensions. Apart from entropy, which is a well-know invariant, three additional invariants are found from an…
We prove convergence of a class of space-time discontinuous Galerkin schemes for scalar hyperbolic conservation laws. Convergence to the unique entropy solution is shown for all orders of polynomial approximation, provided strictly monotone…
We study Hamiltonian difference schemes for scalar conservation laws with monotone flux function and establish the existence of a three-parameter family of periodic travelling waves (wavetrains). The proof is based on an integral equation…
In this paper, we investigate and prove the nonlinear stability of viscous shock wave solutions of a scalar viscous conservation law, using the methods developed for general systems of conservation laws by Howard, Mascia, Zumbrun and…