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Painlevé Test and a Self-Similar Solution of the Kinetic Model
We study a one-dimensional system of equations for a discrete gas model (the McKean system). The McKean system is the Boltzmann kinetic equation of a...
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An Improved Blow-Up Criterion for the Magnetohydrodynamics with the Hall and Ion-Slip Effects
In this work, we consider the magnetohydrodynamics system with the Hall and ion-slip effects in ℝ 3 . The main result is a sufficient condition for...
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Analytical Solutions to a Model of Inviscid Liquid-gas Two-phase Flow with Cylindrical Symmetry and Free Boundary
In this paper, we consider the free boundary value problem for a model of inviscid liquid-gas two-phase flow with cylindrical symmetry. For...
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Uniformly Time-independent L∞ Estimate for a One-dimensional Hydrodynamic Model of Semiconductors
It is well known that the a-priori, uniformly time-independent L ∞ estimate of solutions is the key point to ensure the large time behavior and the...
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The Generalized Riemann Problem for a Chromatography System
The generalized Riemann problem for a model of chromatography system in a conservative form is considered. The unique local solution in the class of...
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High Speed Flight and Partial Differential Equations
Aircraft comes out at the beginning of the last century. Accompanied by the progress of high speed flight the theory of partial differential...
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Global Classical Solutions and the Classical Limit of the Non-Relativistic Vlasov-Darwin System with Small Initial Data
We investigate the global classical solutions of the non-relativistic Vlasov-Darwin system with generalized variables (VDG) in three dimensions. We...
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Global Instability of Multi-Dimensional Plane Shocks for Isothermal Flow
In this paper, we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the...
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Asymptotic growth bounds for the Vlasov-Poisson system with radiation dam**
We consider asymptotic behaviors of the Vlasov-Poisson system with radiation dam** in three space dimensions. For any smooth solution with compact...
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The Stability of the Delta Wave to Pressureless Euler Equations with Viscous and Flux Perturbations
This paper is concerned with the pressureless Euler equations with viscous and flux perturbations. The existence of Riemann solutions to the...
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Reflection and Refraction of Waves Across an Interface of Two-phase Flow
We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase transition. The refraction-reflection phenomena are...
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A Note on the Linear Stability of the Steady State of a Nonlinear Renewal Equation with a Parameter
In this article we consider a variant of age-structured nonlinear Lebowitz-Rubinow equation. We study the linear stability of this equation near the...
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Exact Solutions of Generalized Riemann Problem for Nonhomogeneous Shallow Water Equations
In this paper, we consider quasilinear hyperbolic system of balance laws describing one-dimensional nonhomogeneous shallow water equations with...
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Some special self-similar solutions for a model of inviscid liquid-gas two-phase flow
In this article, we are concerned with analytical solutions for a model of inviscid liquid-gas two-phase flow. On the basis of Yuen’s works [25,...
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Time-Periodic Solutions to Quasilinear Hyperbolic Systems on General Networks
For quasilinear hyperbolic systems on general networks with time-periodic boundary-interface conditions with a dissipative structure, the existence...
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On the Rate of Stabilization of Solutions to the Cauchy Problem for the Godunov–Sultangazin System with Periodic Initial Data
In this paper, we examine a one-dimensional system of equations for a discrete gas model (the Godunov–Sultangazin system). The Godunov–Sultangazin...
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Global L∞ Solutions to System of Isentropic Gas Dynamics in a Divergent Nozzle with Friction
In this article, we study the global L ∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a...
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Large Time Behavior of Solution to Nonlinear Dirac Equation in 1+1 Dimensions
This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in R 1+1 . It is shown that the solution will...
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Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner
The two-dimensional (2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar...
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Convergence Rates to Nonlinear Diffusive Waves for Solutions to Nonlinear Hyperbolic System
This article is involved with the asymptotic behavior of solutions for nonlinear hyperbolic system with external friction. The global existence of...