@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} } @article {1999, title = {Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws}, journal = {Indiana Univ. Math. J. 48 (1999), no. 1, 43--84}, number = {SISSA;96/97/M}, year = {1999}, publisher = {Indiana University}, abstract = {The paper is concerned with the qualitative structure of entropy solutions to a strictly hyperbolic, genuinely nonlinear system of conservation laws. We first give an accurate description of the local and global wave-front structure of a BV solution, generated by a front tracking algorithm.}, doi = {10.1512/iumj.1999.48.1524}, url = {http://hdl.handle.net/1963/3374}, author = {Alberto Bressan and Philippe G. LeFloch} }