@article {2000,
title = {A Uniqueness Condition for Hyperbolic Systems of Conservation Laws},
journal = {Discrete Contin. Dynam. Systems 6 (2000) 673-682},
number = {SISSA;88/98/M},
year = {2000},
publisher = {American Institute of Mathematical Sciences},
abstract = {Consider the Cauchy problem for a hyperbolic $n\\\\times n$ system of conservation laws in one space dimension: $$u_t+f(u)_x=0, u(0,x)=\\\\bar u(x).\\\\eqno(CP)$$ Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions $u=u(t,x)$ which have bounded variation along a suitable family of space-like curves.},
url = {http://hdl.handle.net/1963/3195},
author = {Alberto Bressan and Marta Lewicka}
}
@article {1998,
title = {Uniqueness for discontinuous ODE and conservation laws},
journal = {Nonlinear Analysis 34 (1998) 637-652},
number = {SISSA;26/97/M},
year = {1998},
publisher = {Elsevier},
abstract = {Consider a scalar O.D.E. of the form $\\\\dot x=f(t,x),$ where $f$ is possibly discontinuous w.r.t. both variables $t,x$. Under suitable assumptions, we prove that the corresponding Cauchy problem admits a unique solution, which depends H\\\\\\\"older continuously on the initial data.\\nOur result applies in particular to the case where $f$ can be written in the form $f(t,x)\\\\doteq g\\\\big( u(t,x)\\\\big)$, for some function $g$ and some solution $u$ of a scalar conservation law, say $u_t+F(u)_x=0$. In turn, this yields the uniqueness and continuous dependence of solutions to a class of $2\\\\times 2$ strictly hyperbolic systems, with initial data in $\\\\L^\\\\infty$.},
doi = {10.1016/S0362-546X(97)00590-7},
url = {http://hdl.handle.net/1963/3699},
author = {Alberto Bressan and Wen Shen}
}
@article {1995,
title = {Unique solutions of 2x2 conservation laws with large data},
journal = {Indiana Univ. Math. J. 44 (1995), no. 3, 677-725},
number = {SISSA;73/95/M},
year = {1995},
publisher = {Indiana University Mathematics Journal},
abstract = {For a 2x2 hyperbolic system of conservation laws, we first consider a Riemann problem with arbitrarily large data. A stability assumption is introduced, which yields the existence of a Lipschitz semigroup of solutions, defined on a domain containing all suitably small BV perturbations of the Riemann data. We then establish a uniqueness result for large BV solutions, valid within the same class of functions where a local existence theorem can be proved.},
doi = {10.1512/iumj.1995.44.2004},
url = {http://hdl.handle.net/1963/975},
author = {Alberto Bressan and Rinaldo M. Colombo}
}
@article {1989,
title = {Upper semicontinuous differential inclusions without convexity},
journal = {Proc. Amer. Math. Soc. 106 (1989), no. 3, 771-775},
number = {SISSA;74/88/M},
year = {1989},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/670},
author = {Alberto Bressan and Arrigo Cellina and Giovanni Colombo}
}