01332nas a2200121 4500008004100000245014300041210006900184260002100253520085000274100002301124700001201147856005101159 2014 en d00aGlobal Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension0 aGlobal Structure of Admissible BV Solutions to Piecewise Genuine bTaylor & Francis3 a
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.
1 aBianchini, Stefano1 aYu, Lei uhttp://urania.sissa.it/xmlui/handle/1963/3469400286nas a2200085 4500008004300000245004900043210004900092100002300141856003600164 2006 en_Ud 00aGlimm interaction functional for BGK schemes0 aGlimm interaction functional for BGK schemes1 aBianchini, Stefano uhttp://hdl.handle.net/1963/177000342nas a2200097 4500008004100000245006700041210006400108260001300172100002300185856003600208 2001 en d00aA Glimm type functional for a special Jin-Xin relaxation model0 aGlimm type functional for a special JinXin relaxation model bElsevier1 aBianchini, Stefano uhttp://hdl.handle.net/1963/1355