TY - JOUR T1 - Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems JF - J. Differential Equations 172 (2001) 59-82 Y1 - 2001 A1 - Paolo Baiti A1 - Philippe G. LeFloch A1 - Benedetto Piccoli PB - Elsevier UR - http://hdl.handle.net/1963/3113 U1 - 1220 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws JF - J. Differential Equations 151 (1999) 345-372 Y1 - 1999 A1 - Debora Amadori A1 - Paolo Baiti A1 - Philippe G. LeFloch A1 - Benedetto Piccoli AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/3312 U1 - 1018 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws JF - Indiana Univ. Math. J. 48 (1999), no. 1, 43--84 Y1 - 1999 A1 - Alberto Bressan A1 - Philippe G. LeFloch AB - 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. PB - Indiana University UR - http://hdl.handle.net/1963/3374 U1 - 956 U2 - Mathematics U3 - Functional Analysis and Applications ER -