@article {2014,
title = {Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension},
number = {Communications in Partial Differential Equations;Volume 39; issue 2; pp. 244-273;},
year = {2014},
publisher = {Taylor \& Francis},
abstract = {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.},
doi = {10.1080/03605302.2013.775153},
url = {http://urania.sissa.it/xmlui/handle/1963/34694},
author = {Stefano Bianchini and Lei Yu}
}
@article {2014,
title = {Structure of entropy solutions to general scalar conservation laws in one space dimension},
number = {SISSA;11/2014/MATE},
year = {2014},
institution = {SISSA},
url = {http://hdl.handle.net/1963/7259},
author = {Stefano Bianchini and Lei Yu}
}
@mastersthesis {2013,
title = {The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension},
year = {2013},
school = {SISSA},
abstract = {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:
{\textbullet} SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws.
{\textbullet} Global structure of admissible BV solutions to strict hyperbolic conservation laws.},
author = {Lei Yu}
}
@article {2012,
title = {Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension},
number = {arXiv.org;1211.3526},
year = {2012},
institution = {SISSA},
abstract = {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 $u$.},
keywords = {Hyperbolic conservation laws, Wave-front tracking, Global structure of solution.},
url = {http://hdl.handle.net/1963/6316},
author = {Stefano Bianchini and Lei Yu}
}