%0 Report
%D 2012
%T Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension
%A Stefano Bianchini
%A Lei Yu
%K Hyperbolic conservation laws, Wave-front tracking, Global structure of solution.
%X The paper gives an accurate description of the qualitative structure of an admissible BV solution to a strictly hyperbolic, piecewise genuinely nonlinear system of conservation laws. We prove that there are a countable set $\\\\Theta$ which contains all interaction points and a family of countably many Lipschitz curves $\\\\T$ such that outside $\\\\T\\\\cup \\\\Theta$ $u$ is continuous, and along the curves in $\\\\T$, u has left and right limit except for points in $\\\\Theta$. This extends the corresponding structural result in \\\\cite{BL,Liu1} for admissible solutions.\\r\\n\\r\\nThe proof is based on approximate wave-front tracking solutions and a proper selection of discontinuity curves in the approximate solutions, which converge to curves covering the discontinuities in the exact solution $u$.
%I SISSA
%G en
%U http://hdl.handle.net/1963/6316
%1 6225
%2 Mathematics
%3 Functional Analysis and Applications
%4 1
%# MAT/05 ANALISI MATEMATICA
%$ Submitted by Lei Yu (yulei@sissa.it) on 2012-11-15T08:50:10Z\\nNo. of bitstreams: 1\\nglobal structure of solutions to PWGN hyperbolic conservation laws.pdf: 452219 bytes, checksum: 85bd51fc08fa53a087cee8aec2b9544a (MD5)