@article {2003,
	title = {A lemma and a conjecture on the cost of rearrangements},
	journal = {Rend. Sem. Mat. Univ. Padova 110 (2003) 97-102},
	number = {SISSA;13/2003/M},
	year = {2003},
	publisher = {Universit{\`a} di Padova},
	abstract = {Consider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement.},
	url = {http://hdl.handle.net/1963/2914},
	author = {Alberto Bressan}
}
@article {2002,
	title = {On a Lyapunov functional relating shortening curves and viscous conservation laws},
	journal = {Nonlinear Anal. 51 (2002) 649-662},
	number = {SISSA;123/99/M},
	year = {2002},
	publisher = {Elsevier},
	abstract = {We study a nonlinear functional which controls the area swept by a curve moving in the plane in the direction of curvature. In turn, this yields a priori estimates on solutions to a class of parabolic equations and of scalar viscous conservation laws. A further application provides an estimate on the \\\"change of shape\\\" of a BV solution to a scalar conservation law.},
	doi = {10.1016/S0362-546X(01)00848-3},
	url = {http://hdl.handle.net/1963/1337},
	author = {Stefano Bianchini and Alberto Bressan}
}
@article {1999,
	title = {L-1 stability estimates for n x n conservation laws},
	journal = {Arch. Ration. Mech. Anal.  149  (1999),  no. 1, 1--22},
	number = {SISSA;80/98/M},
	year = {1999},
	publisher = {Springer},
	abstract = {Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws, each characteristic field being linearly degenerate or genuinely nonlinear. In this paper we explicitly define a functional $\\\\Phi=\\\\Phi(u,v)$, equivalent to the $L^1$ distance, which is {\textquoteleft}almost decreasing\\\', i.e., $\\\\Phi(u(t),v(t))-\\\\Phi(u(s),v(s))\\\\leq\\\\break O (\\\\epsilon){\textperiodcentered}(t-s)$ for all $t>s\\\\geq 0$, for every pair of $\\\\epsilon$-approximate solutions $u,v$ with small total variation, generated by a wave-front-tracking algorithm. The small parameter $\\\\epsilon$ here controls the errors in the wave speeds, the maximum size of rarefaction fronts and the total strength of all non-physical waves in $u$ and in $v$. From the above estimate, it follows that front-tracking approximations converge to a unique limit solution, depending Lipschitz continuously on the initial data, in the $L^1$ norm. This provides a new proof of the existence of the standard Riemann semigroup generated by an $n\\\\times n$ system of conservation laws.\\\'\\\'},
	doi = {10.1007/s002050050165},
	url = {http://hdl.handle.net/1963/3373},
	author = {Alberto Bressan and Tai-Ping Liu and Tong Yang}
}
