检索结果-南通市图书馆

Existence in the Large for Pressure-Gradient System

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2022年第4期43卷 509-522页

作者： Shuxin ZHANG Zejun WANG Department of Mathematics Nanjing University of Aeronautics and AstronauticsKey Laboratory of Mathematical and High Performance Computing of Air Vehicles(NUAA)MIITNanjing 210016China

In this paper,the authors use glimm scheme to study the global existence of BV solutions to Cauchy problem of the pressure-gradient system with large initial *** this end,some important properties of the shock curves of the pressure-gradient system in the Riemann invariant coordinate system and verify that the shock curves satisfy Diperna’s conditions(see[Diperna,R.J.,Existence in the large for quasilinear hyperbolic conservation laws,***.,52(3),1973,244–257])are *** they construct the approximate solution sequence through glimm *** establishing accurate local interaction estimates,they prove the boundedness of the approximate solution sequence and its total variation.

关键词： Pressure-gradient system Riemann problem Diperna’s conditions glimm scheme BV space

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2014年第1期34卷 1-38页

作者：陈贵强肖长国张永前 Mathematical Institute University of Oxford School of Mathematical Sciences Fudan University

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.

关键词： combustion detonation wave stability glimm scheme fractional-step su- personic flow reacting Euler flow Riemann problem entropy solutions two-dimensional steady flow asymptotic behavior

THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2023年第5期43卷 2263-2278页

作者：黎前锋张永前 School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice East China Normal UniversityShanghai 200241China School of Mathematical Sciences Fudan UniversityShanghai 200433China

This paper focusses on a peeling phenomenon governed by a nonlinear wave equation with a free *** the hypotheses that the total variation of the intial data and the boundary data are small,the global existence of a weak solution to the nonlinear problem(1.1)-(1.3)is proven by a modified glimm *** regularity of the peeling front is established,and the asymptotic behaviour of the obtained solution and the peeling front at infinity is also studied.

关键词： peeling model nonlinear wave solution free boundary glimm scheme

STABILITY OF STEADY MULTI-WAVE CONFIGURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2018年第5期38卷 1485-1514页

作者： Gui-Qiang G.CHEN Matthew RIGBY Mathematical Institute University of OxfordOxfordOX2 6GGU

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem （initial value problem） in the flow direction, and then develop a modified glimm difference scheme and identify a glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than 1, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.

关键词： stability multi-wave configuration vortex sheet entropy wave shock wave BV perturbation full Euler equations steady wave interactions glimm scheme

INITIAL-BOUNDARY PROBLEM FOR THE 1-D EULER-BOLTZMANN EQUATIONS IN RADIATION HYDRODYNAMICS

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2018年第1期38卷 34-56页

作者：张晶张永前 School of Mathematical Sciences Fudan University

We study the initial-boundary value problem for the one dimensional Euler-Boltzmann equation with reflection boundary condition. For initial data with small total variation, we use a modified glimm scheme to construct the global approximate solutions （U△t,d, I△t,d） and prove that there is a subsequence of the approximate solutions which is convergent to the global solution.

关键词： global existence Euler-Boltzmann equations initial-boundary glimm scheme

Global Entropy Solutions of the Cauchy Problem for Nonhomogeneous Relativistic Euler System

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2006年第5期27卷 473-494页

作者： Yachun LI Anjiao WANG Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 China

We analyze the 2 × 2 nonhomogeneous relativistic Euler equations for perfect fluids in special relativity. We impose appropriate conditions on the lower order source terms and establish the existence of global entrop... 详细信息

关键词： Relativistic Euler system Entropy solutions Riemann solutions glimm scheme

Numerical Study of Singularity Formation in Relativistic Euler Flows

在线全文

学校读者我要写书评

暂无评论

Communications in Computational Physics 2014年第7期16卷 348-364页

作者： Pierre A.Gremaud Yi Sun Department ofMathematics North Carolina State UniversityRaleighNC27695USA Department of Mathematics University of South CarolinaColumbiaSC 29208USA.

The formation of singularities in relativistic flows is not well *** solutions to the relativistic Euler equations are known to have a finite lifespan;the possible breakdown mechanisms are shock formation,violation of the subluminal conditions andmass *** propose a new hybrid glimm/centralupwind scheme for relativistic *** scheme is used to numerically investigate,for a family of problems,which of the above mechanisms is involved.

关键词： Relativistic Euler equations singularity formation glimm scheme central-upwind scheme hybrid method.

Weak Solutions of the Isothermal Bipolar Hydrodynamic Model for Semiconductors with Large Data

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Wuhan University Journal of Natural Sciences 2014年第1期19卷 62-70页

作者： MAO Jianfeng School of Mathematics and Statistics Hubei Science University

This paper is devoted to weak solutions of Cauchy problem to the isothermal bipolar hydrodynamic model with large data. The model takes the bipolar Euler-Poisson form, with electric field and relaxation terms added to the momentum equations. Using glimm scheme to the hyperbolic part and the standard theory to the ordinary differential equations, we first construct the approximation solutions, then from the facts that the total charge is quasi-conservation, we can obtain a uniform estimate of the total variation of the electric field, which allows to prove the L∞ estimate of densities and velocities, and the convergence of the scheme. Then we can prove the global existence of weal solution to Cauchy problem with large data.

关键词： weak solution isothermal bipolar hydrodynamic model glimm scheme