1.

BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NONSTRICTLY HYPERBOLIC SYSTEMS





徐玉梅《数学物理学报(A辑)》,2006年第Z1期


In this article, the author considers the Cauchy problem for quasilinear nonstrict ly hyperbolic systems and obtain a blowup result for the C1 solution to the Cauchy problem with weaker decaying initial data.

2.

BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NONSTRICTLY HYPERBOLIC SYSTEMS





徐玉梅《数学物理学报(A辑)》,2006年第26卷第6期


In this article, the author considers the Cauchy problem for quasilinear nonstrictly hyperbolic systems and obtain a blowup result for the C^{1} solution to the Cauchy problem with weaker decaying initial data.

3.

GLOBAL EXISTENCE OF WEAKLY DISCONTIN UOUS SOLUTIONS TO THE CAUCHY PROBLEM WITH A KIND OF NONSMOOTH INITIAL DATA FOR QUASILINEAR HYPERBOLIC SYSTEMS 被引次数：4





LI Tatsien WANG Libin《数学年刊B辑(英文版)》,2004年第25卷第3期


The authors consider the Cauchy problem with a kind of nonsmooth initial datafor quasilinear hyperbolic systems and obtain a necessary and sufficient condition toguarantee the existence and uniqueness of global weakly discontinuous solution.

4.

BREAKDOWN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS





Xu Yumei《高校应用数学学报(英文版)》,2006年第21卷第4期


This paper deals with the asymptotic behavior of the lifespan of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying initial data, and obtains a blowup result for C1 solution to Cauchy problem.

5.

A NOTE ON THE GENERALIZED RIEMANN PROBLEM~*





李大潜《数学物理学报(B辑英文版)》,1991年第3期


§ 1. Introduction The Riemann problem for the quasilinear hyperbolic system of conservation laws

6.

GLOBAL CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH WEAK LINEAR DEGENERACY 被引次数：7





ZHOU Yi《数学年刊B辑(英文版)》,2004年第25卷第1期


§1. Introduction and Main Results Consider the following ?rst order quasilinear strictly hyperbolic system ?u ?u A(u) = 0, (1.1) ?t ?xwhere u = (u1, ···,un)T is the unknown vector function of (t,x) and A(u) is an n×n matrixwith suitably smooth elements aij(u) (i,j = 1, ···,n). By the de?nition …

7.

LIFESPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOWDECAY INITIAL DATA 被引次数：7





KONG Dexing《数学年刊B辑(英文版)》,2000年第21卷第4期


The author considers the lifespan of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with “slow“ decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the lifespan of classical solutions are given in the casethat the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.11.3 in [2] are still valid for this kind of initial data.

8.

LIFESPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOWDECAY INITIAL DATA





KONG Dexing《数学年刊A辑(中文版)》,2000年第4期


The author considers the lifespan of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with “slow” decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the lifespan of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.11.3 in [2] are still valid for this kind of initial data.

9.

Exact Boundary Controllability and Exact Boundary Observability for a Coupled System of Quasilinear Wave Equations





Long HU Fanqiong JI Ke WANG《数学年刊B辑(英文版)》,2013年第34卷第4期


Based on the theory of semiglobal classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1D quasilinear wave equations with various types of boundary conditions.

10.

INITIAL BOUNDARY VALUE PROBLEMS FOR QUASILINEAR HYPERBOLICPARABOLIC COUPLED SYSTEMS IN HIGHER DIMENSIONAL SPACES





郑宋穆《数学年刊B辑(英文版)》,1983年第4期


The initial bounary value problem for quasilinear hyperbolicparabolic coupled systemsin higher dimensional spaces,which arises in many mechanical problems is considered.Underthe assumptions that the hyperbolic part of the coupled system is a quasilinear symmetrichyperbolic system and the parabolic part is a quasilinear parabolic system of second orderand suitble asstunptions of smoothness and compatibiliy conditions,the existence anduniqueness of local smooth solution is proved in the cases that the boundary of domain isnoncharacteristic or uniformly characteristic with respect to the hyperbolic part.As an application,the existence and uniqueness of local smooth solution for the initialboundary problem of the radiation hydrodynamic system,as well as of the viscous compressiblehydrodynamic system,with solid wall boundary,is obtained.

11.

具常重特征的非齐次拟线性双曲组的整体弱间断解





郭飞《数学研究及应用》,2012年第32卷第6期


This paper considers the Cauchy problem with a kind of nonsmooth initial data for general inhomogeneous quasilinear hyperbolic systems with characteristics with constant multiplicity. Under the matching condition, based on the refined fomulas on the decomposition of waves, we obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution to the Cauchy problem.

12.

Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems with One Weakly Linearly Degenerate Characteristic





Peng QU Cunming LIU《数学年刊B辑(英文版)》,2012年第33卷第3期


For a kind of partially dissipative quasilinear hyperbolic systems without ShizutaKawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissi...

13.

Local Smooth Solutions to the 3Dimensional IsentropicRelativistic Euler equations?





Yongcai GENG Yachun LI《数学年刊B辑(英文版)》,2014年第35卷第2期


The authors consider the local smooth solutions to the isentropic relativistic Euler equations in （3＋1）dimensional spacetime for both nonvacuum and vacuum cases. The local existence is proved by symmetrizing the system and applying the Friedrichs LaxKato theory of symmetric hyperbolic systems. For the nonvacuum case, according to Godunov, firstly a strictly convex entropy function is solved out, then a suitable sym metrizer to symmetrize the system is constructed. For the vacuum case, since the coefficient matrix blowsup near the vacuum, the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.

14.

GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE TYPICAL FREE BOUNDARY PROBLEM FOR GERENAL QUASILINEAR HYPERBOLIC SYSTEMS AND ITS APPLICATIONS





李大潜 赵彦淳《数学年刊B辑(英文版)》,1990年第1期


In this paper the authors prove the existence and uniqueness of global classicalsolutions to the typical free boundary problem for general quasilinear hyperbolic systems.As an application,a unique global discontinuous solution only containing n shocks ont≥0 is obtained for a class of generalized Riemann problem for the quasilinear hyperbolicsystem of n conservation laws.

15.

GLOBAL CLASSICAL SOLUTIONS WITH SMALL INITIAL TOTAL VARIATION FOR QUASILINEAR HYPERBOLIC SYSTEMS





YAN Ping《数学年刊B辑(英文版)》,2002年第23卷第3期


By means of the continuous Glimm functional,a proof is given on the global existence ofclassical solutions to Cauchy problem for general first order quasilinear hyperbolic systems withsmall initial total rariation.

16.

一类对角形拟线性双曲型方程组空间周期解的破裂





葛菊《数学季刊》,2008年第23卷第1期


In this paper,we discuss the blowup of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form,and make the accurate estimate of lifespan.These results in this paper extend the conclusion[1～3].

17.

DESCRIPTION AND WENO NUMERICAL APPROXIMATION TO NONLINEAR WAVES OF A MULTICLASS TRAFFIC FLOW LWR MODEL





张鹏 戴世强 刘儒勋《应用数学和力学(英文版)》,2005年第26卷第6期


A strict proof of the hyperbolicity of the multiclass LWR (LighthillWhithamRichards) traffic flow model, as well as the descriptions on those nonlinear waves characterized in the traffic flow problems were given. They were mainly about the monotonicity of densities across shocks and in rarefactions. As the system had no characteristic decomposition explicitly, a high resolution and higher order accuracy WENO( weighted essentially nonoscillatory) scheme was introduced to the numerical simulation, which coincides with the analytical description.

18.

GLOBAL SMOOTH SOLUTIONS FOR A CLASS OF QUASILINEAR HYPERBOLIC SYSTEMS WITH DISSIPATIVE TERMS 被引次数：1





李大潜 秦铁虎《数学年刊B辑(英文版)》,1985年第2期


In this paper the authors prove the existence and uniqueness of global smooth solutionsto the Cauchy problem for quasilinear hyperbolic systems with some kinds of dissipativeterms.

19.

OSCILLATION OF SOLUTIONS OF THE SYSTEMS OF QUASILINEAR HYPERBOLIC EQUATION UNDER NONLINEAR BOUNDARY CONDITION





邓立虎 穆春来《数学物理学报(B辑英文版)》,2007年第27卷第3期


Sufficient conditions are obtained for the oscillation of solutions of the systems of quasilinear hyperbolic differential equation with deviating arguments under nonlinear boundary condition.

20.

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS





Li Tatsien Rao Bopeng《数学物理学报(B辑英文版)》,2009年第29卷第4期


We consider first order quasilinear hyperbolic systems with vertical characteristics. It was shown in [4] that such systems can be exactly controllable with the help of internal controls applied to the equations corresponding to zero eigenvalues. However, it is possible that, for physical or engineering reasons, we can not put any control on the equations corresponding to zero eigenvalues. In this paper, we will establish the exact controllability only by means of physically meaningfnl internal controls applied to the equations corresponding to nonzero eigenvalues. We also show the exact controllability for a very simplified model by means of switching controls.
