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 - Structure of entropy solutions to general scalar conservation laws in one space dimension
Y1 - 2014
A1 - Stefano Bianchini
A1 - Lei Yu
PB - SISSA
UR - http://hdl.handle.net/1963/7259
U1 - 7305
U2 - Mathematics
U4 - -1
ER -
TY - THES
T1 - The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension
Y1 - 2013
A1 - Lei Yu
AB - This thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws.
PB - SISSA
U1 - 7210
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
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 -