Related papers: Entropy conditions for scalar conservation laws wi…
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…
Here we provide uniqueness of vanishing viscosity solutions to sub-Riemannian mean curvature flow problem, which was known only far from characteristic points or under special symmetry condition. We employ vanishing viscosity approach and…
We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both conservative and non conservative…
We analyze the well-posedness of a flow-plate interaction considered in [22, 24]. Specifically, we consider the Kutta-Joukowski boundary conditions for the flow [20, 28, 26], which ultimately give rise to a hyperbolic equation in the…
We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader…
We generalize the previously obtained Kru\v{z}kov-type uniqueness result for the initial-boundary value problem for the chemical flood conservation law system to the case of an almost arbitrary flow function, not restricted by the S-shaped…
In geophysical flows such as large-scale ocean dynamics, the vertical viscosity is often much smaller than the horizontal viscosity. This anisotropy makes it natural to ask whether solutions of the full anisotropic compressible…
We study the uniqueness of solutions of the initial-boundary value problem in the quarter-plane for the chemical flood conservation law system in the class of piece-wise $\mathcal C^1$-smooth functions under certain restrictions. The…
In this paper, we propose a novel development in the context of entropy stable finite-volume/finite-difference schemes. In the first part, we focus on the construction of high-order entropy conservative fluxes. Already in [LMR2002], the…
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…
For a class of nonconservative hyperbolic systems of partial differential equations endowed with a strictly convex mathematical entropy, we formulate the initial value problem by supplementing the equations with a kinetic relation…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
We introduce a generalization of relative entropy derived from the Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for the map…
Bousso has conjectured that in any spacetime satisfying Einstein's equation and satisfying the dominant energy condition, the "entropy flux" S through any null hypersurface L generated by geodesics with non-positive expansion starting from…
Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux and with initial data being a sum of periodic function and a function…
We consider the scalar conservation law in one space dimension with a genuinely nonlinear flux. We assume that an appropriate velocity function depending on the entropy solution of the conservation law is given for the comprising particles,…
In this paper, we study the vanishing viscosity limit of one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity, to the isentropic compressible Euler equations. Based on several new uniform…
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the…
Compressible (full) potential flow is expressed as an equivalent first-order system of conservation laws for density $\rho$ and velocity $v$. Energy $E$ is shown to be the only nontrivial entropy for that system in multiple space…
In the present contribution, we investigate first-order nonlinear systems of partial differential equations which are constituted of two parts: a system of conservation laws and non-conservative first order terms. Whereas the theory of…