Debora Amadori

Initial-boundary value problems for nonlinear systems of conservation laws

Abstract. The system of conservation laws ¶¶ut+[f(u)]x= 0 (1)¶ is considered on a domain

The one-dimensional Hughes model for pedestrian flow: Riemann—type solutions

\{(t,x);\ t\ge 0,\ x> \Psi(t)\}

Global weak solutions for systems of balance laws

, for a continuous map

On a Model of Multiphase Flow

\Psi:[0,\infty)\rightarrow {\bfR}

AN INTEGRO-DIFFERENTIAL CONSERVATION LAW ARISING IN A MODEL OF GRANULAR FLOW

, subject to the initial condition ¶¶

Global Existence of Large BV Solutions in a Model of Granular Flow

u(0,x)=\bar u(x),\quad x> \Psi(0)

A Hyperbolic Model of Multiphase Flow

. (2) ¶¶ We prove two global existence theorems for (1) - (2) for two distinct types of boundary conditions, with data of small total variation.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO CONSERVATION LAWS WITH PERIODIC FORCING

Abstract This paper deals with a coupled system consisting of a scalar conservation law and an eikonal equation, called the Hughes model. Introduced in [24], this model attempts to describe the motion of pedestrians in a densely crowded region, in which they are seen as a ‘thinking’ (continuum) fluid. The main mathematical difficulty is the discontinuous gradient of the solution to the eikonal equation appearing in the flux of the conservation law. On a one dimensional interval with zero Dirichlet conditions (the two edges of the interval are interpreted as ‘targets’), the model can be decoupled in a way to consider two classical conservation laws on two sub-domains separated by a turning point at which the pedestrians change their direction. We shall consider solutions with a possible jump discontinuity around the turning point. For simplicity, we shall assume they are locally constant on both sides of the discontinuity. We provide a detailed description of the local-in-time behavior of the solution in terms of a ‘global’ qualitative property of the pedestrian density (that we call ‘relative evacuation rate’), which can be interpreted as the attitude of the pedestrians to direct towards the left or the right target. We complement our result with explicitly computable examples.

Error Estimates for Well-Balanced Schemes on Simple Balance Laws

Abstract We are concerned with global, weak solutions to the Cauchy problem for a (strictly hyperbolic) system of balance laws, u t +[F(u)] x =g(u) , u(0, x)=u 0 (x) . Assume that the initial data has small total variation. We give a sufficient condition for global existence of solutions in BV. Such a condition generalizes the one required by Dafermos and Hsiao in their paper [1].

Derivation and analysis of a fluid-dynamical model in thin and long elastic vessels

We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity, and the mass density fraction of the vapor in the fluid. For a class of initial data having large total variation we prove the global existence of solutions to the Cauchy problem.