Related papers: Well-Balanced Schemes for the Initial Boundary Val…
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…
Consider a scalar conservation law with discontinuous flux \begin{equation*}\tag{1} \quad u_{t}+f(x,u)_{x}=0, \qquad f(x,u)= \begin{cases} f_l(u)\ &\text{if}\ x<0,\\ f_r(u)\ & \text{if} \ x>0, \end{cases} \end{equation*} where $u=u(x,t)$ is…
In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then,…
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…
We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume…
In this article, we propose a second-order central scheme of the Nessyahu-Tadmor-type for a class of scalar conservation laws with discontinuous flux and present its convergence analysis. Since solutions to problems with discontinuous flux…
We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair $(\eta(u),q(u))$ with…
We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishes the convergence of monotone and first-order finite volume…
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 $…
The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…
We derive and analyze well-posed, energy- and entropy-stable boundary conditions (BCs) for the two-dimensional linear and nonlinear rotating shallow water equations (RSWE) in vector invariant form. The focus of the study is on subcritical…
We propose a semidiscrete scheme for approximation of entropy solutions of one-dimensional scalar conservation laws with nonnegative initial data. The scheme is based on the concept of particle paths for conservation laws and can be…
We consider the Cauchy problem for a $n\times n$ strictly hyperbolic system of balance laws $$ \{{array}{c} u_t+f(u)_x=g(x,u), x \in \mathbb{R}, t>0 u(0,.)=u_o \in L^1 \cap BV(\mathbb{R}; \mathbb{R}^n), | \lambda_i(u)| \geq c > 0 {for all}…
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,…
We present a class of numerical schemes for two-dimensional systems of nonlocal conservation laws, which are based on utilizing well-known monotone numerical flux functions after suitably approximating the nonlocal terms. The considered…
The existing paradox between theory and computational experiment for weak solutions of systems of conservation laws in higher space dimensions is arguably resolved. Apparently successful computations are identified with underlying…
We consider four definitions of solution to the initial-boundary value problem for a scalar balance laws in several space dimensions. These definitions are generalised to the same most general framework and then compared. The first aim of…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…
We study a degenerate parabolic-hyperbolic equation with zero flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite…
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…