A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved...A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.展开更多
In this paper,we study the global smooth solutions of the Cauchy problem for two important nonstrictly quasilinear hyperbolic systems.i.e.,the isentropic gas dynamics system in Euler coordinates (Ⅰ) and the rotationa...In this paper,we study the global smooth solutions of the Cauchy problem for two important nonstrictly quasilinear hyperbolic systems.i.e.,the isentropic gas dynamics system in Euler coordinates (Ⅰ) and the rotational degeneracy of hyperbolic systems of conservation laws(Ⅱ).sufficient conditions which guarantee the existence of gloats smooth solutions of the Cauchy problems (Ⅰ) and (Ⅱ) are obtained by employing the characteristic method.展开更多
The interaction of shock waves is investigated for the following nonstrictly hyperbolic system: [GRAPHICS] The interaction of shock waves is complicated, with new types of shock waves, and new singula rities in the de...The interaction of shock waves is investigated for the following nonstrictly hyperbolic system: [GRAPHICS] The interaction of shock waves is complicated, with new types of shock waves, and new singula rities in the dependence of interaction on the relative positions of the three states separated by shock waves. Several ideas are introduced to helo organize and clarify the new phenomena.展开更多
This paper studies the interaction of elementary waves including delta-shock waves on two boundaries for a hyperbolic system of conservation laws. The solutions of the initialboundary value problem for the system are ...This paper studies the interaction of elementary waves including delta-shock waves on two boundaries for a hyperbolic system of conservation laws. The solutions of the initialboundary value problem for the system are constructively obtained. In the problem the initialboundary data are in piecewise constant states.展开更多
This paper is a extension of [1], [3]. By the method in [1], the authors prove the global existence of the solutions of the Riemann problem for a class of 2 × 2 nonstrictly hyperbolic conservation laws.
In this paper,we apply the discontinuous Galerkin method with LaxWendroff type time discretizations(LWDG)using the weighted essentially nonoscillatory(WENO)limiter to solve a multi-class traffic flow model for an inho...In this paper,we apply the discontinuous Galerkin method with LaxWendroff type time discretizations(LWDG)using the weighted essentially nonoscillatory(WENO)limiter to solve a multi-class traffic flow model for an inhomogeneous highway.This model is a kind of hyperbolic conservation law with spatially varying fluxes.The numerical scheme is based on a modified equivalent system which is written as a“standard”hyperbolic conservation form.Numerical experiments for both the Riemann problem and the traffic signal control problem are presented to show the effectiveness of the method.展开更多
文摘A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.
文摘In this paper,we study the global smooth solutions of the Cauchy problem for two important nonstrictly quasilinear hyperbolic systems.i.e.,the isentropic gas dynamics system in Euler coordinates (Ⅰ) and the rotational degeneracy of hyperbolic systems of conservation laws(Ⅱ).sufficient conditions which guarantee the existence of gloats smooth solutions of the Cauchy problems (Ⅰ) and (Ⅱ) are obtained by employing the characteristic method.
文摘The interaction of shock waves is investigated for the following nonstrictly hyperbolic system: [GRAPHICS] The interaction of shock waves is complicated, with new types of shock waves, and new singula rities in the dependence of interaction on the relative positions of the three states separated by shock waves. Several ideas are introduced to helo organize and clarify the new phenomena.
基金Supported by the National Natural Science Foundation of China (10671120)
文摘This paper studies the interaction of elementary waves including delta-shock waves on two boundaries for a hyperbolic system of conservation laws. The solutions of the initialboundary value problem for the system are constructively obtained. In the problem the initialboundary data are in piecewise constant states.
文摘This paper is a extension of [1], [3]. By the method in [1], the authors prove the global existence of the solutions of the Riemann problem for a class of 2 × 2 nonstrictly hyperbolic conservation laws.
基金supported by NSFC grant 10671091 and JSNSF BK2006511.
文摘In this paper,we apply the discontinuous Galerkin method with LaxWendroff type time discretizations(LWDG)using the weighted essentially nonoscillatory(WENO)limiter to solve a multi-class traffic flow model for an inhomogeneous highway.This model is a kind of hyperbolic conservation law with spatially varying fluxes.The numerical scheme is based on a modified equivalent system which is written as a“standard”hyperbolic conservation form.Numerical experiments for both the Riemann problem and the traffic signal control problem are presented to show the effectiveness of the method.
