Related papers: An exactly conservative particle method for one di…
We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the…
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 $…
We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well-posed: it admits a unique solution, characterized by a kinetic formulation…
We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present…
Modified versions of the Schr\"{o}dinger equation have been proposed in order to incorporate the description of measurement processes into the mathematical structure of quantum theory. Typically, these proposals introduce new physical…
A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…
We consider a fully asymmetric one-dimensional model with mass-conserving coalescence. Particles of unit mass enter at one edge of the chain and coalescence while performing a biased random walk towards the other edge where they exit. The…
We study the following class of scalar hyperbolic conservation laws with discontinuous fluxes: \partial_t\rho+\partial_xF(x,\rho)=0. The main feature of such a conservation law is the discontinuity of the flux function in the space variable…
This paper proposes and validates two new particle regularization techniques for the Smoothed Particle Hydrodynamics (SPH) numerical method to improve its stability and accuracy for free surface flow simulations. We introduce a general form…
We prove a uniqueness result for BV solutions of scalar conservation laws with discontinuous flux in several space dimensions. The proof is based on the notion of kinetic solution and on a careful analysis of the entropy dissipation along…
We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…
In this paper, we introduce and discuss an exactly energy-conserving Particle-in-Cell method for arbitrary curvilinear coordinates. The flexibility provided by curvilinear coordinates enables the study of plasmas in complex-shaped domains…
This paper deals with an optimal control problem and describes the reachable set for the scalar 1-D conservation laws with discontinuous flux. Regarding the optimal control problem we first prove the existence of a minimizer and then we…
Nonlinear scalar conservation laws are traditionally viewed as transport equations. We take instead the viewpoint of these PDEs as continuity equations with an implicitly defined velocity field. We show that a weak solution is the entropy…
We study the $L^2$-type contraction property of large perturbations around shock waves of scalar viscous conservation laws with strictly convex fluxes in one space dimension. The contraction holds up to a shift, and it is measured by a…
The paper considers one-dimensional flows of polytropic (calorically ideal) gas. These flows include three cases of gas dynamics: plain one-dimensional flows (one-dimensional space), radially symmetric flows in two-dimensional space and…
This paper describes the reachable set and resolves an optimal control problem for the scalar conservation laws with discontinuous flux. We give a necessary and sufficient criteria for the reachable set. A new backward resolution has been…
In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite…
We study aspects of the hydrodynamics of one-dimensional totally asymmetric K-exclusion, building on the hydrodynamic limit of Seppalainen (1999). We prove that the weak solution chosen by the particle system is the unique one with maximal…
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…