Related papers: Conservation laws with nonlocal velocity -- the si…
We study the limiting behavior of the solutions to a class of conservation laws with vanishing nonlinear diffusion and dispersion terms. We prove the convergence to the entropy solution of the first order problem under a condition on the…
We investigate one-dimensional scalar balance laws with singular convolution-type source terms. Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in ${\bf L}^2(\mathbb{R})$,…
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…
We consider multidimensional conservation laws perturbed by multiplicative L\'{e}vy noise. We establish existence and uniqueness results for entropy solutions. The entropy inequalities are formally obtained by the It\^{o}-L\'{e}vy chain…
We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…
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 propose a new approach for crowd motion models where the density constraint can only slow down the motion of each agent, with no effect on those agents who are not in a saturated area or who have no saturated density ''in front'' of…
In this article, we propose a MUSCL-Hancock-type second-order scheme for the discretization of a general class of non-local conservation laws and present its convergence analysis. The main difficulty in designing a MUSCL-Hancock-type scheme…
We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial…
We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergence of the regularized solutions toward discontinuous…
This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) property to manifolds, by deriving conditions on the flux of…
We obtain several new regularity results for solutions of scalar conservation laws satisfying the genuine nonlinearity condition. We prove that the solutions are continuous outside of the jump set, which is codimension one rectifiable. We…
We investigate the initial-value problem for the relativistic Euler equations governing isothermal perfect fluid flows, and generalize an approach introduced by LeFloch and Shelukhin in the non-relativistic setting. We establish the…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
We are concerned with the global existence of finite-energy entropy solutions of the one-dimensional compressible Euler equations with (possibly) damping, alignment forces, and nonlocal interactions: Newtonian repulsion and quadratic…
In this article, we develop what are, to the best of our knowledge, the first negative results for scalar conservation laws. We begin with explicit examples where bounded initial data leads to $L^{\infty}$ blow-up despite flux regularity.…
We are concerned with spherically symmetric solutions to the Euler equations for the multi-dimensional compressible fluids, which have many applications in diverse real physical situations. The system can be reduced to one dimensional…
We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution…
We consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L^2 perturbations of shock wave solutions to the Riemann problem using the relative entropy…
We consider the local well-posedness of the one-dimensional nonisentropic Euler equations with moving physical vacuum boundary condition. The physical vacuum singularity requires the sound speed to be scaled as the square root of the…