In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relati...In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relativistic Euler equations are shown. The collision of two shocks, two centered rarefaction waves, a shock and a rarefaction wave yield corresponding ransmitted waves. The overtaking of two shocks appears a transmitted shock wave, together with a reflected centered rarefaction wave.展开更多
In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the init...In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states. Furthermore, it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter ε goes to zero.展开更多
We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-...We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves,we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the n-D shock waves. The asymptotic behaviors with geometric structures are also proved.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
基金Project supported by the National Natural Science Foundation of China (Grant No.10671120)
文摘In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relativistic Euler equations are shown. The collision of two shocks, two centered rarefaction waves, a shock and a rarefaction wave yield corresponding ransmitted waves. The overtaking of two shocks appears a transmitted shock wave, together with a reflected centered rarefaction wave.
基金Sponsored by National Natural Science Foundation of China (10901077)China Postdoctoral Science Foundation (201003504+1 种基金 20090451089)Shandong Provincial Doctoral Foundation (BS2010SF006)
文摘In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states. Furthermore, it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter ε goes to zero.
基金partly supported by the National Natural Science Foundation of China (Grant11701551 and Grant 11971024)partly supported by the National Natural Science Foundation of China (Grant 11471332)。
文摘We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves,we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the n-D shock waves. The asymptotic behaviors with geometric structures are also proved.
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.
