00436nas a2200121 4500008004300000245008800043210006900131260001300200100001700213700002500230700002300255856003600278 2001 en_Ud 00aUniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems0 aUniqueness of classical and nonclassical solutions for nonlinear bElsevier1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311301145nas a2200145 4500008004300000245007900043210006900122260001300191520067400204100002000878700001700898700002500915700002300940856003600963 1999 en_Ud 00aNonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws0 aNonclassical Shocks and the Cauchy Problem for Nonconvex Conserv bElsevier3 aThe 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.1 aAmadori, Debora1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/331200739nas a2200121 4500008004300000245010400043210006900147260002300216520029600239100002100535700002500556856003600581 1999 en_Ud 00aStructural stability and regularity of entropy solutions to hyperbolic systems of conservation laws0 aStructural stability and regularity of entropy solutions to hype bIndiana University3 aThe 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.1 aBressan, Alberto1 aLeFloch, Philippe G. uhttp://hdl.handle.net/1963/3374