%0 Journal Article %J J. Differential Equations 172 (2001) 59-82 %D 2001 %T Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems %A Paolo Baiti %A Philippe G. LeFloch %A Benedetto Piccoli %B J. Differential Equations 172 (2001) 59-82 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3113 %1 1220 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-15T10:27:54Z\\nNo. of bitstreams: 1\\nuniqueness.pdf: 278381 bytes, checksum: d70f89c690a2695e7b44e73737a6aff8 (MD5) %R 10.1006/jdeq.2000.3869 %0 Journal Article %J J. Differential Equations 151 (1999) 345-372 %D 1999 %T Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws %A Debora Amadori %A Paolo Baiti %A Philippe G. LeFloch %A Benedetto Piccoli %X 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. %B J. Differential Equations 151 (1999) 345-372 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3312 %1 1018 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-20T11:49:26Z\\nNo. of bitstreams: 1\\nNonclassical_shocks.pdf: 261875 bytes, checksum: bd41bb6490895996b965941b1eeb6797 (MD5) %R 10.1006/jdeq.1998.3513 %0 Journal Article %J Indiana Univ. Math. J. 48 (1999), no. 1, 43--84 %D 1999 %T Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws %A Alberto Bressan %A Philippe G. LeFloch %X 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. %B Indiana Univ. Math. J. 48 (1999), no. 1, 43--84 %I Indiana University %G en_US %U http://hdl.handle.net/1963/3374 %1 956 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-01T09:02:14Z\\nNo. of bitstreams: 1\\nStructural_stability.pdf: 3175042 bytes, checksum: c04760cbf353315764f5aa8e879b0a62 (MD5) %R 10.1512/iumj.1999.48.1524