TY - RPRT
T1 - Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension
Y1 - 2012
A1 - Stefano Bianchini
A1 - Lei Yu
KW - Hyperbolic conservation laws, Wave-front tracking, Global structure of solution.
AB - 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 $u$.
PB - SISSA
UR - http://hdl.handle.net/1963/6316
U1 - 6225
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -