01325nas a2200121 4500008004100000245014300041210006900184260002100253520084300274100002301117700001201140856005101152 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 aThe 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/1963/3469400395nas a2200109 4500008004100000245009400041210006900135260001000204100002300214700001200237856003600249 2014 en d00aStructure of entropy solutions to general scalar conservation laws in one space dimension0 aStructure of entropy solutions to general scalar conservation la bSISSA1 aBianchini, Stefano1 aYu, Lei uhttp://hdl.handle.net/1963/725900932nas a2200109 4500008004100000245011500041210006900156260001000225520044500235100001200680856013000692 2013 en d00aThe structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension0 astructure and regularity of admissible BV solutions to hyperboli bSISSA3 aThis 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.1 aYu, Lei uhttps://www.math.sissa.it/publication/structure-and-regularity-admissible-bv-solutions-hyperbolic-conservation-laws-one-space01371nas a2200133 4500008004100000245014300041210006900184260001000253520081800263653008501081100002301166700001201189856003601201 2012 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 bSISSA3 aThe 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 $u$.10aHyperbolic conservation laws, Wave-front tracking, Global structure of solution.1 aBianchini, Stefano1 aYu, Lei uhttp://hdl.handle.net/1963/6316