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We investigate the uniqueness of entropy solution to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint. The constraint is imposed with a singular pressure. Given initial data for which the standard self-similar solution consists of one shock or one shock and one rarefaction wave, it turns out that there exist infinitely many admissible weak solutions. This extends the result of Markfelder and Klingenberg in [S. Markfelder and C. Klingenberg, The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock, Arch. Ration. Mech. Anal. 227(3) (2018) 967–994] for classical Euler system to the case with maximum density constraint. Also some estimates on the density of these solutions are given to describe the behavior of solutions near congestion. [ABSTRACT FROM AUTHOR]

Abstract: A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the density and velocity orientation. Short-range repulsion is included through a singular pressure which becomes infinite at the jamming density. The singular limit of infinite pressure stiffness leads to phase transitions from compressible to incompressible dynamics. The paper proposes an Asymptotic-Preserving scheme which takes care of the singular pressure while preventing the breakdown of the Courant–Friedrichs–Lewy (CFL) stability condition near congestion. It relies on a relaxation approximation of the system and an elliptic formulation of the pressure equation. Numerical simulations of impinging clusters show the efficiency of the scheme to treat congestions. A two-fluid variant of the model provides a model of path formation in crowds. [Copyright &y& Elsevier]

Abstract: In this paper, we study the numerical simulations for Euler system with maximal density constraint. This model is developed in with the constraint introduced into the system by a singular pressure law, which causes the transition of different asymptotic dynamics between different regions. To overcome these difficulties, we adapt and implement two asymptotic preserving (AP) schemes originally designed for low Mach number limit to our model. These schemes work for the different dynamics and capture the transitions well. Several numerical tests both in one dimensional and two dimensional cases are carried out for our schemes. [Copyright &y& Elsevier]

Abstract: The sharp decay estimate of rarefaction waves in terms of a partial ordering among positive measures is not only interesting in itself but also crucial in the study of convergence rate of vanishing viscosity approximations, cf. Bressan and Yang (2004) . Such an estimate is well established for genuinely nonlinear system of conservation laws, cf. Bressan and Yang (2004) . But similar result is not available for non-genuinely nonlinear system. In this paper, we give a new measure about the rarefaction waves. In addition, a sharp decay estimate of the new measure is given for the cubic nonlinear system of conservation laws. [Copyright &y& Elsevier]

Abstract: In this paper, we study the stability of a single transonic shock wave solution to the hyperbolic conservation laws with a resonant moving source. Compared with the previous results [W.-C. Lien, Hyperbolic conservation laws with a moving source, Comm. Pure Appl. Math. 52 (9) (1999) 1075–1098; T.P. Liu, Nonlinear stability and instability of transonic flows through a nozzle, Comm. Math. Phys. 83 (2) (1982) 243–260] on this stability problem, in this paper, the transonic ith shock is assumed to be relatively strong and stable in the sense of Majda. Then the framework of [M. Lewicka, stability of patterns of non-interacting large shock waves, Indiana Univ. Math. J. 49 (4) (2000) 1515–1537; M. Lewicka, Stability conditions for patterns of noninteracting large shock waves, SIAM J. Math. Anal. 32 (5) (2001) 1094–1116 (electronic)] can be applied. A new criterion is obtained to test whether such a shock is time asymptotically stable or not. And by constructing the Liu–Yang functional, one can prove the stability of the shock under the stability condition. This is an extension of the result [S.-Y. Ha, T. Yang, stability for systems of hyperbolic conservation laws with a resonant moving source, SIAM J. Math. Anal. 34 (5) (2003) 1226–1251 (electronic); W.-C. Lien, Hyperbolic conservation laws with a moving source, Comm. Pure Appl. Math. 52 (9) (1999) 1075–1098] to a more general case. [Copyright &y& Elsevier]

Abstract: We study the convergence rate of Glimm scheme for general systems of hyperbolic conservation laws without the assumption that each characteristic field is either genuinely nonlinear or linearly degenerate. We first give a sharper estimate of the error arising from the wave tracing argument by a careful analysis of the interaction between small waves. With this key estimate, the convergence rate is shown to be , which is sharper compared to given in [T. Yang, Convergence rate of Glimm scheme for general systems of hyperbolic conservation laws, Taiwanese J. Math. 7 (2) (2003) 195–205]. However, it is still slower than given in [A. Bressan, A. Marson, Error bounds for a deterministic version of the Glimm scheme, Arch. Ration. Mech. Anal. 142 (2) (1998) 155–176] for systems with each characteristic field being genuinely nonlinear or linearly degenerate. Here s is the mesh size and α is any positive constant. [Copyright &y& Elsevier]

Columbianetin acetate (CE) is one of the effective components of Angelica pubescens. So far, the specific role and molecular mechanism of CE in pancreatic cancer are not clear. Thus, this study aimed to explore the specific mechanism of CE on pancreatic cancer. The target genes combined with CE were predicted through the PharmMapper database and the 3D molecular structure of CE. Then, the Cancer Genome Atlas (TCGA) and Cistrome data browser (DB) databases were used to screen Meiotic nuclear divisions 1 (MND1)-related genes, transcription factors, and transcription factor data sets, and the intersection of the above data sets. The "limma" package in the R and gene expression profiling interactive analysis (GEPIA) databases were used to analyze the correlation and survival difference between the target genes and MND1 to predict the degree of association between CE and MND1. Western blotting and RT-PCR experiments revealed the regulatory relationship among CE, E2F1, and MND1 at the cellular level. The specific effects of CE on pancreatic cancer cells were explored through CCK8, wound healing, migration, and flow cycle experiments. E2F1, also the predictive transcription factor of MND1, was also the predictive target protein of CE. At the same time, E2F1 and MND1 were closely related in pancreatic tissue. In the cell function experiment, CE and interference with E2F1 expression could reduce the gene and protein expression of MND1, which was closely associated with cell proliferation, migration, and cycle development. Similarly, interfering with the expression of mnd1 can also inhibit the further development of tumor cells. CE may inhibit the development of pancreatic cancer cells by reducing the expression of MND1. This implies that CE may be a potential novel agent for the treatment of pancreatic cancer. [ABSTRACT FROM AUTHOR]