@article {2006,
	title = {Infinite Horizon Noncooperative Differential Games},
	number = {SISSA;31/2005/M},
	year = {2006},
	abstract = {For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability.},
	doi = {10.1016/j.jde.2006.01.005},
	url = {http://hdl.handle.net/1963/1720},
	author = {Alberto Bressan and Fabio Simone Priuli}
}
@article {2006,
	title = {An instability of the Godunov scheme},
	journal = {Comm. Pure Appl. Math. 59 (2006) 1604-1638},
	number = {arXiv.org;math/0502125v1},
	year = {2006},
	abstract = {We construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes.},
	doi = {10.1002/cpa.20141},
	url = {http://hdl.handle.net/1963/2183},
	author = {Alberto Bressan and Helge Kristian Jenssen and Paolo Baiti}
}
@article {2003,
	title = {An ill posed Cauchy problem for a hyperbolic system in two space dimensions},
	number = {SISSA;12/2003/M},
	year = {2003},
	publisher = {Universit{\`a} di Padova},
	abstract = {The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed.},
	url = {http://hdl.handle.net/1963/2913},
	author = {Alberto Bressan}
}
