@article {2005,
	title = {An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation},
	number = {SISSA;27/2005/M},
	year = {2005},
	abstract = {In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) <= κ {\textperiodcentered} J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.},
	url = {http://hdl.handle.net/1963/1719},
	author = {Alberto Bressan and Massimo Fonte}
}
@article {1999,
	title = {Oleinik type estimates and uniqueness for n x n conservation laws},
	journal = {J. Differential Equations  156  (1999),  no. 1, 26--49},
	number = {SISSA;150/97/M},
	year = {1999},
	publisher = {Elsevier},
	abstract = {Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of $u$ in a forward neighborhood of each point in the $t\\\\text{-}x$ plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleinik in the scalar case.},
	doi = {10.1006/jdeq.1998.3606},
	url = {http://hdl.handle.net/1963/3375},
	author = {Alberto Bressan and Paola Goatin}
}
