阻碍集、拟双曲性与线性横截性

对Mane′、SackerSell、Selgrade的拟双曲性线性横截性理论做一整理,提供一种较简洁的处理方式。最后一节解释这一理论如何对应于廖山涛先生的文章《阻碍集(Ⅰ)》,因而本文也可视为对《阻碍集(Ⅰ)》的一个解说。

Quasilinear Hyperbolic Conservation Laws with Relaxation

In this paper, we investigate the relaxation phenomenon for quasilinear hyperbolic conservation laws, and obtain global smooth solutions and the life span of classical solutions to its Cauchy problem. These results shows that the relaxation admits the effects of dissipation.

Blow Up of Periodic Solutions to a Class of Quasilinear Hyperbolic Systems in Diagonal Form

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

Existence and Life Span of Periodic Solutions for the First Order Quasilinear Hyperbolic Equations

In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship of dissipation and smoothness of periodic solutions.

A Class of the Quasilinear Hyperbolic Equations with the Inhomogenous Terms

In this paper,we discuss a class of the quasillinear hyperbolic equations with the inhomogeneous terms: u_■+σ(v)+2α(t)u=0.v_■-u-0 Under the certain of hypothesis.we prove the globally existence theorems of the smooth solutions for its Cauchy problem.

On a Quasilinear Hyperbolic System Relative to an Atmospheric Model on the Transition of Water Defined on the Whole Space

In this paper we study a quasi-linear hyperbolic system, with some integral operators, arising from an atmospheric model on the transition of water. By using the method of characteristics and a fixed point argument, we prove a theorem of existence, uniqueness and continuous dependence on data, in Lipschitz class, of the solution to this problem.

SEMI-GLOBAL C^1 SOLUTION TO THE MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

By means of an equivalent invariant form of boundary conditions, the authors get the exis- tence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with general nonlinear boundary conditions.

LIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATALIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATA

The author considers the life-span 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 life-span 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 1.1-1.3 in [2] are still valid for this kind of initial data.

GLOBAL CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH WEAK LINEAR DEGENERACY

Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ?t ?x t = 0 : u = f(x). We let M = sup |f (x)| < +∞. x∈R The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant ε independent of M, such that the above Cauchy problem admits a unique global C1 solution u = u(t,x) for all t ∈ R, provided that +∞ |f (x)|dx ≤ ε, ?∞ +∞ ε |f(x)|dx ≤ . M∞

ＬＯＣＡＬＥＸＡＣＴＢＯＵＮＤＡＲＹＣＯＮＴＲＯＬＬＡＢＩＬＩＴＹＦＯＲＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭＳ

For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.

Strong (Weak) Exact Controllability and Strong (Weak) Exact Observability for Quasilinear Hyperbolic Systems

In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the relationship between them.

Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems

Based on the theory of semi-global C 1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.

GLOBAL EXISTENCE OF WEAKLY DISCONTIN UOUS SOLUTIONS TO THE CAUCHY PROBLEM WITH A KIND OF NON-SMOOTH INITIAL DATA FOR QUASILINEAR HYPERBOLIC SYSTEMS

The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution.

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

Based on the theory of semi-global 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 1-D quasilinear wave equations with various types of boundary conditions.

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

For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.

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

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

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH ZERO EIGENVALUES

For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internai controls acting on a part of equations in the system.

SOME REMARKS ON THE NULL CONDITION FOR NONLINEAR ELASTODYNAMIC SYSTEM

The author derives the same null condition as in [1] for the nonlinear elastodynamic system in a simpler way and proves the equivalence of the null conditions introduced in [1] and [7] respectively.

Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems.Under the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in Arch.Rational Mech.Anal.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.

POINTWISE ESTIMATES OF SOLUTIONS TO CAUCHY PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamental solutions. It gives a sharp pointwise estimates of the solutions on domam under consideration. Specially, the estimate is precise near each characteristic direction.