Let $u_t+f(u)_x=0$ be a strictly hyperbolic, genuinely nonlinear system of conservation laws of Temple class. In this paper, a continuous semigroup of solutions is constructed on a domain of $L^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the $L^1$ distance. Moreover, we show that a weak solution of the Cauchy problem coincides with the corresponding semigroup trajectory if and only if it satisfies an entropy condition of Oleinik type, concerning the decay of positive waves.

%B Differential Integral Equations 13 (2000) 1503-1528 %I Khayyam Publishing %G en_US %U http://hdl.handle.net/1963/3256 %1 1445 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-06T13:16:51Z\\nNo. of bitstreams: 1\\nTemple.pdf: 221742 bytes, checksum: a13773198af84c04068cf3021f12d3c8 (MD5) %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 %0 Journal Article %J Differential Integral Equations 10 (1997), no. 3, 401-418 %D 1997 %T The semigroup generated by a temple class system with large data %A Paolo Baiti %A Alberto Bressan %X We consider the Cauchy problem $$u_t + [F(u)]_x=0, u(0,x)=\\\\bar u(x) (*)$$ for a nonlinear $n\\\\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of (*) that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation. %B Differential Integral Equations 10 (1997), no. 3, 401-418 %I SISSA Library %G en %U http://hdl.handle.net/1963/1023 %1 2833 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:49Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. %D 1997 %T Shift-differentiability of the flow generated by a conservation law %A Alberto Bressan %A Graziano Guerra %X The paper introduces a notion of \\\"shift-differentials\\\" for maps with values in the space BV. These differentials describe first order variations of a given functin $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition. %B Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. %I SISSA Library %G en %U http://hdl.handle.net/1963/1033 %1 2823 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:57Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 %D 1997 %T Structural stability for time-optimal planar sytheses %A Alberto Bressan %A Benedetto Piccoli %B Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 %I SISSA Library %G en %U http://hdl.handle.net/1963/997 %1 2859 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:28Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Mat. Contemp. 10 (1996) 21-74 %D 1996 %T The semigroup approach to systems of conservation laws %A Alberto Bressan %B Mat. Contemp. 10 (1996) 21-74 %I Sociedade Brasileira de Matematica %G en %U http://hdl.handle.net/1963/1037 %1 2819 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:00Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995