TY - JOUR T1 - Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension Y1 - 2014 A1 - Stefano Bianchini A1 - Lei Yu AB -

The paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

PB - Taylor & Francis UR - http://urania.sissa.it/xmlui/handle/1963/34694 U1 - 34908 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Glimm interaction functional for BGK schemes Y1 - 2006 A1 - Stefano Bianchini UR - http://hdl.handle.net/1963/1770 U1 - 2774 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Glimm type functional for a special Jin-Xin relaxation model JF - Ann. Inst. H. Poincare\\\' Anal. Non Lineaire 18 (2001), no. 1, 19-42 Y1 - 2001 A1 - Stefano Bianchini PB - Elsevier UR - http://hdl.handle.net/1963/1355 U1 - 3100 U2 - Mathematics U3 - Functional Analysis and Applications ER -