Related papers: Initial Data Identification for Conservation Laws …
In this paper we establish well-posedness for scalar conservation laws on closed manifolds M endowed with a constant or a time-dependent Riemannian metric for initial values in L^\infty(M). In particular we show the existence and uniqueness…
We consider a min-max problem for strictly concave conservation laws on a 1-1 network, with inflow controls acting at the junction. We investigate the minimization problem for a functional measuring the total variation of the flow of the…
We prove that adapted entropy solutions of scalar conservation laws with discontinuous flux are stable with respect to changes in the flux under the assumption that the flux is strictly monotone in u and the spatial dependency is piecewise…
This paper is concerned with entropy solutions of scalar conservation laws of the form $\partial_{t}u+\diver f=0$ in $\mathbb{R}^d\times(0,\infty)$. The flux $f=f(x,u)$ depends explicitly on the spatial variable $x$. Using an extension of…
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 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,…
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…
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…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
We consider the abstract initial value problem for the system of evolution equations which describe motion of micropolar fluids with heat conduction in a bounded domain. This problem has uniquely a mild solution locally in time for general…
We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on conservation laws with diffusion. Using this space, we…
We are concerned with a new solution formula and its applications to the analysis of properties of entropy solutions of the Cauchy problem for one-dimensional scalar hyperbolic conservation laws, wherein the flux functions exhibit convexity…
We study the entropy solution for a class of systems of nonlocal conservation laws in which the convective flux is convoluted with a kernel in both spatial and temporal variables. This formulation models the flux dependence on the solution…
Here we consider scalar conservation law in one space dimension with strictly convex flux. Goal of this paper is to study two problems. First problem is to know the profile of the entropy solution. In spite of the fact that, this was…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
It is known that Flux Corrected Transport algorithms can produce entropy-violating solutions of hyperbolic conservation laws. Our purpose is to design flux correction with maximal antidiffusive fluxes to obtain entropy solutions of scalar…
We build a finite volume scheme for the scalar conservation law $\partial_t u + \partial_x (H(x, u)) = 0$ with bounded initial condition for a wide class of flux function $H$, convex with respect to the second variable. The main idea for…
We study the problem of recovery both the attenuation $a$ and the source $f$ in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there are natural Hamiltonian flow that determines which…
We investigate the well-posedness of scalar conservation laws whose flux depends on the solution both pointwise and nonlocally through integral averages. Our analysis is based on a fixed-point formulation, in which the nonlocal dependence…
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flow. In this paper, we propose a novel…