Andrea Marson

On the Attainable Set for Scalar Nonlinear Conservation Laws with Boundary Control

We consider the initial value problem with boundary control for a scalar nonlinear conservation law \begin{equation*} u_t+[f(u)]_x=0,\qquad\qquad u(0,x)=0,\qquad u(\cdot,0)= \tilde u\in{\cal U},\tag{

A variational calculus for discontinuous solutions of systems of conservation laws

\ast

A Hölder continuous ODE related to traffic flow

} \end{equation*} on the domain

Scalar non-linear conservation laws with integrable boundary data

\Omega=\{(t,x)\in\real^2: t\geq 0, x\geq 0\}

On the Attainable Set for a Scalar Nonconvex Conservation Law

. Here

Well-posedness for non genuinely nonlinear conservation laws

u=u(t,x)

Conservation Laws and O.D.E.s. A Traffic Problem

is the state variable,

Special issue on contemporary topics in conservation laws

{\cal U}

Front Tracking for Non Genuinely Nonlinear Conservation Laws

is a set of bounded boundary data regarded as controls, and

A maximum principle for optimally controlled systems of conservation laws

f