@article {2009,
	title = {On the convergence of viscous approximations after shock interactions},
	journal = {Discrete Contin. Dyn. Syst. 23 (2009) 29-48},
	year = {2009},
	publisher = {American Institute of Mathematical Sciences},
	abstract = {We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.},
	doi = {10.3934/dcds.2009.23.29},
	url = {http://hdl.handle.net/1963/3412},
	author = {Alberto Bressan and Carlotta Donadello}
}
@article {2006,
	title = {Conservative Solutions to a Nonlinear Variational Wave Equation},
	journal = {Comm. Math. Phys. 266 (2006) 471-497},
	number = {arXiv.org;math/0502058v1},
	year = {2006},
	abstract = {We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values.},
	doi = {10.1007/s00220-006-0047-8},
	url = {http://hdl.handle.net/1963/2184},
	author = {Alberto Bressan and Zheng Yuxi}
}
@article {2004,
	title = {On the convergence rate of vanishing viscosity approximations},
	journal = {Comm. Pure Appl. Math. 57 (2004) 1075-1109},
	number = {SISSA;60/2003/M},
	year = {2004},
	publisher = {Wiley},
	abstract = {Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves.},
	doi = {10.1002/cpa.20030},
	url = {http://hdl.handle.net/1963/2915},
	author = {Alberto Bressan and Tong Yang}
}
@article {2002,
	title = {A center manifold technique for tracing viscous waves},
	journal = {Commun. Pure Appl. Anal. 1 (2002) 161-190},
	number = {SISSA;85/2001/M},
	year = {2002},
	publisher = {American Institute of Mathematical Sciences},
	abstract = {In this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data.},
	url = {http://hdl.handle.net/1963/3075},
	author = {Stefano Bianchini and Alberto Bressan}
}
@article {2001,
	title = {A case study in vanishing viscosity},
	journal = {Discrete Cont. Dyn. Syst. 7 (2001) 449-476},
	year = {2001},
	publisher = {American Institute of Mathematical Sciences},
	url = {http://hdl.handle.net/1963/3091},
	author = {Stefano Bianchini and Alberto Bressan}
}
@article {2000,
	title = {On the convergence of Godunov scheme for nonlinear hyperbolic systems},
	journal = {Chinese Ann. Math. B, 2000, 21, 269},
	number = {SISSA;15/00/M},
	year = {2000},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1473},
	author = {Alberto Bressan and Helge Kristian Jenssen}
}
@article {1991,
	title = {A class of absolute retracts of dwarf spheroidal galaxies},
	journal = {Proc.Amer.Math.Soc. 112 (1991), no.2, 413},
	number = {SISSA;79/89/M},
	year = {1991},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/837},
	author = {Alberto Bressan and Arrigo Cellina and Andrzej Fryszkowski}
}
