Paolo Baiti

Lower semicontinuity of weighted path length in BV

We establish some basic lower semicontinuity properties for a class of weighted metrics in BV. These Riemann-type metrics, uniformly equivalent to the L 1 distance, are defined in terms of the Glimm interaction potential. They are relevant in the study of nonlinear hyperbolic systems of conservation laws, being contractive w.r.t. the corresponding flow of solutions.

Global existence of solutions for a multi-phase flow: A drop in a gas-tube

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.

Global existence of solutions for a multi-phase flow: A bubble in a liquid tube and related cases

In this paper we study the problem of the global existence (in time) of weak, entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models the dynamics of phase transitions in an isothermal fluid; in Lagrangian coordinates, the phase interfaces are represented as stationary contact discontinuities. We focus on the persistence of solutions consisting in three bulk phases separated by two interfaces. Under some stability conditions on the phase configuration and by a suitable front tracking algorithm we show that, if the BV-norm of the initial data is less than an explicit (large) threshold, then the Cauchy problem has global solutions.

Non-classical global solutions for a class of scalar conservation laws

We consider the Cauchy problem for a class of scalar conservation laws with flux having a single inflection point. We prove existence of global weak solutions satisfying a single entropy inequality together with a kinetic relation, in a class of bounded variation functions. The kinetic relation is obtained by the travelling-wave criterion for a regularization consisting of balanced diffusive and dispersive terms. The result is applied to the one-dimensional Buckley-Leverett equation.