10 papers
A Two-Fluxes Stochastic Model of Traffic Waves
Alberto Bressan, Sumantha Kanale Suresha
The paper introduces a stochastic model for the spontaneous formation of traffic waves on a highway. This is formulated in terms of a conservation law with discontinuous, gradient-…
Local Asymptotic Patterns for Viscous Approximations of Conservation Laws
Alberto Bressan, Laura Caravenna, Wen Shen
Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximatio…
A Uniqueness Condition for Conservation Laws with Discontinuous Gradient-Dependent Flux
Alberto Bressan, Wen Shen
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions or , when th…
Uniqueness Domains for Solutions of Hyperbolic Conservation Laws
Alberto Bressan, Elio Marconi, Ganesh Vaidya
For a genuinely nonlinear hyperbolic system of conservation laws, assuming that the initial data have small norm but possibly unbounded total variation…
Generic uniqueness and conjugate points for optimal control problems
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
The paper is concerned with an optimal control problem on , where the dynamics is linear w.r.t.~the control functions. For a terminal cost in a set…
Conservation Laws with Discontinuous Gradient-Dependent Flux: the Stable Case
Debora Amadori, Alberto Bressan, Wen Shen
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions or , when th…
Conservation Laws with Discontinuous Gradient-Dependent Flux: the Unstable Case
Debora Amadori, Alberto Bressan, Wen Shen
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions or , when th…
Generic Solutions to Controlled Balance Laws
Alberto Bressan, Khai T. Nguyen
The paper is concerned with a scalar balance law, where the source term depends on a control function . Given a control , it is prove…
Intermediate Domains for Scalar Conservation Laws
Fabio Ancona, Alberto Bressan, Elio Marconi +1
For a scalar conservation law with strictly convex flux, by Oleinik's estimates the total variation of a solution with initial data decay…
Generic Properties of Conjugate Points in Optimal Control Problems
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
The first part of the paper studies a class of optimal control problems in Bolza form, where the dynamics is linear w.r.t.~the control function. A necessary condition is derived, f…