For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results...For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results by taking a suitable entropy-flux pair （Journal of Differential Equations, 1988, 71（1）： 93-122）. The solutions of the initial-boundary value problem for the system are constructively obtained, in which initial-boundary data are in piecewise constant states. The delta-shock waves appear in their solutions.展开更多
The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number ...The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left（right）-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No.10671120）
文摘For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results by taking a suitable entropy-flux pair （Journal of Differential Equations, 1988, 71（1）： 93-122）. The solutions of the initial-boundary value problem for the system are constructively obtained, in which initial-boundary data are in piecewise constant states. The delta-shock waves appear in their solutions.
基金Supported by the Scientific Research Program of the Higher Education Institution of Xinjiang(XJEDU2011S02)the Ph.D Graduate Start Research Foundation of Xinjiang University Funded Project(No.BS100105 and BS090107)the National Natural Science Foundation of China(11101348)
基金Supported by National Natural Science Foundation of China(Grant No.11361073)
文摘The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left（right）-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis.
