@article {2007,
	title = {BV instability for the Lax-Friedrichs scheme},
	number = {SISSA;100/2004/M},
	year = {2007},
	abstract = {It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.},
	url = {http://hdl.handle.net/1963/2335},
	author = {Paolo Baiti and Alberto Bressan and Helge Kristian Jenssen}
}
@article {2005,
	title = {On the Blow-up for a Discrete Boltzmann Equation in the Plane},
	journal = {Discrete Contin. Dyn. Syst. 13 (2005) 1-12},
	number = {arXiv.org;math/0403047v2},
	year = {2005},
	abstract = {We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed.},
	url = {http://hdl.handle.net/1963/2244},
	author = {Alberto Bressan and Massimo Fonte}
}
@article {2002,
	title = {On the Boundary Control of Systems of Conservation Laws},
	journal = {SIAM J. Control Optim. 41 (2002) 607-622},
	number = {SISSA;50/2001/M},
	year = {2002},
	publisher = {SIAM},
	abstract = {The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.},
	doi = {10.1137/S0363012901392529},
	url = {http://hdl.handle.net/1963/3070},
	author = {Alberto Bressan and Giuseppe Maria Coclite}
}
@article {2000,
	title = {BV estimates for multicomponent chromatography with relaxation},
	journal = {Discrete Contin. Dynam. Systems  6  (2000) 21-38},
	number = {SISSA;122/99/M},
	year = {2000},
	publisher = {SISSA Library},
	abstract = {We consider the Cauchy problem for a system of $2n$ balance laws which arises from the modelling of multi-component chromatography: $$\\\\left\\\\{ \\\\eqalign{u_t+u_x\&=-{1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr v_t\&={1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr}\\\\right. \\\\eqno(1)$$ This model describes a liquid flowing with unit speed over a solid bed. Several chemical substances are partly dissolved in the liquid, partly deposited on the solid bed. Their concentrations are represented respectively by the vectors $u=(u_1,\\\\ldots,u_n)$ and $v=(v_1,\\\\ldots,v_n)$.  We show that, if the initial data have small total variation, then the solution of (1) remains with small variation for all times $t\\\\geq 0$. Moreover, using the $\\\\L^1$ distance, this solution depends Lipschitz continuously on the initial data, with a Lipschitz constant uniform w.r.t.~$\\\\ve$. Finally we prove that as $\\\\ve\\\\to 0$, the solutions of (1) converge to a limit described by the system $$\\\\big(u+F(u)\\\\big)_t+u_x=0,\\\\qquad\\\\qquad v=F(u).\\\\eqno(2)$$  The proof of the uniform BV estimates relies on the application of probabilistic techniques. It is shown that the components of the gradients $v_x,u_x$ can be interpreted as densities of random particles travelling with speed 0 or 1. The amount of coupling between different components is estimated in terms of the expected number of crossing of these random particles. This provides a first example where BV estimates are proved for general solutions to a class of $2n\\\\times 2n$ systems with relaxation.},
	url = {http://hdl.handle.net/1963/1336},
	author = {Alberto Bressan and Wen Shen}
}
@article {2000,
	title = {BV solutions for a class of viscous hyperbolic systems},
	journal = {Indiana Univ. Math. J.  49 (2000) 1673-1714},
	year = {2000},
	publisher = {Indiana University Mathematics Journal},
	doi = {10.1512/iumj.2000.49.1776},
	url = {http://hdl.handle.net/1963/3194},
	author = {Stefano Bianchini and Alberto Bressan}
}
