@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 {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 {2001,
	title = {Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems},
	journal = {J. Differential Equations 172 (2001) 59-82},
	year = {2001},
	publisher = {Elsevier},
	doi = {10.1006/jdeq.2000.3869},
	url = {http://hdl.handle.net/1963/3113},
	author = {Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli}
}
@article {1999,
	title = {Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws},
	journal = {J. Differential Equations 151 (1999) 345-372},
	number = {SISSA;139/97/M},
	year = {1999},
	publisher = {Elsevier},
	abstract = {The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.},
	doi = {10.1006/jdeq.1998.3513},
	url = {http://hdl.handle.net/1963/3312},
	author = {Debora Amadori and Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli}
}
@mastersthesis {1997,
	title = {On Existence and Continuous Dependence for Systems of Conservation Laws},
	year = {1997},
	school = {SISSA},
	keywords = {Conservation laws},
	url = {http://hdl.handle.net/1963/5588},
	author = {Paolo Baiti}
}
@article {1997,
	title = {The semigroup generated by a temple class system with large data},
	journal = {Differential Integral Equations 10 (1997), no. 3, 401-418},
	number = {SISSA;121/95/M},
	year = {1997},
	publisher = {SISSA Library},
	abstract = {We consider the Cauchy problem $$u_t + [F(u)]_x=0, u(0,x)=\\\\bar u(x) (*)$$ for a nonlinear $n\\\\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of (*) that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation.},
	url = {http://hdl.handle.net/1963/1023},
	author = {Paolo Baiti and Alberto Bressan}
}
