In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of sh...In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the vanishing viscosity limit of a family of smooth global solutions for a viscous system of conservation law. We remark that, after the interacting time, not only shocks but also contact discontinuity are generated.展开更多
In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this...In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained.展开更多
基金Xiaoding Shi was supported by National Natural Sciences Foundation of China(11471321)Yan Yong was supported by National Natural Sciences Foundation of China(11201301)
文摘In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the vanishing viscosity limit of a family of smooth global solutions for a viscous system of conservation law. We remark that, after the interacting time, not only shocks but also contact discontinuity are generated.
基金X.Li’s research was supported in part by NSFC(11301344)Y.Yong’sresearch was supported in part by NSFC(11201301)
文摘In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained.
