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.

PB - Khayyam Publishing UR - http://hdl.handle.net/1963/3256 U1 - 1445 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 - TY - JOUR T1 - The semigroup generated by a temple class system with large data JF - Differential Integral Equations 10 (1997), no. 3, 401-418 Y1 - 1997 A1 - Paolo Baiti A1 - Alberto Bressan AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1023 U1 - 2833 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shift-differentiability of the flow generated by a conservation law JF - Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. Y1 - 1997 A1 - Alberto Bressan A1 - Graziano Guerra AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1033 U1 - 2823 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Structural stability for time-optimal planar sytheses JF - Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 Y1 - 1997 A1 - Alberto Bressan A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/997 U1 - 2859 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The semigroup approach to systems of conservation laws JF - Mat. Contemp. 10 (1996) 21-74 Y1 - 1996 A1 - Alberto Bressan PB - Sociedade Brasileira de Matematica UR - http://hdl.handle.net/1963/1037 U1 - 2819 U2 - Mathematics U3 - Functional Analysis and Applications ER -