多维非线性拟双曲方程外初边值问题

本文利用Ｌａｐｌａｃｅ方程解的正则性定理，建立一般非线性拟双曲型方程，Ｌ［ｕ］＝ｕｔｔ－Δｕｔ－ｎ／Σｉｊ＝１ａｉｊ（ｕＤｘｔｕ）Ｕｘｉｘｊ＋ｂ（ｕ，Ｄｘｔｕ）＝０的一个能量不等式和叠代格式，然后利用Ｓｏｂｏｌｅｘ空间中的弱紧性原理，证明方程（１）的外初边值问题古典整体解存在唯一性和衰减性质。     

可换四元数空间中某些双曲型方程的Riemann-Hilbert边值问题

考察了在可交换四元数空间(基元为1,i,j,k满足条件i~2=j~2=-1,ij=ji= k)中的某些双曲型方程的Riemann-Hilbert边值问题,分别在不同的情况下获得了问题的可解条件和通解.     

具耗散项拟线性双曲型方程组的边值问题

本文考虑具耗散项一阶拟线性双曲型方程组的具有自由边界的典型自由边值问题．在一些合理假设下,证明了其经典解的整体存在性定理．     

一类非线性双曲型方程初边值问题解的爆破

该文给出一类非线性双曲型方程初边值问题解爆破的充分条件, 并证明问题局部解的存在性与唯一性     

非线性伪双曲方程初边值问题整体广义解

本文证明了一类非线性伪双曲方程初边值问题整体广义解的存在唯一性．     

一类高阶非线性双曲型方程初边值问题解的爆破

本文研究一类高阶非线性双曲型方程的初边值问题，证明问题局部广义解的存在性与唯一性，同时给出解爆破的充分条件。     

广义Захаров方程组的初边值问题

本文用积分估计的方法对于一类更广泛的Захаров方程组的初边值问题（其中一维问题为第三初边值问题，二维为第一初边值问题），证明了广义解的存在性。     

四阶线性双曲型方程混合边值问题的迭代解法

本根据一个函数方程的解，用迭代法导出了一类四阶线性双曲型方程混合边值问题的古典解。     

四阶线性双曲型方程混合边值问题的迭代解法

本文根据一个函数方程的解，用迭代法导出了一类四阶线性双曲型方程混合边值问题的古典解     

一类拟线性双曲型方程组混合初-边值问题的半整体C~1解

本文证明了具零特征且形式更广泛的一类拟线性双曲型方程组的具有一般非线性边界条件的混合初 一边值问题半整体C1解的存在唯一性.     

Boundary Value Problems for Degenerate Hyperbolic Systems of First Order Equations

In this paper we discuss some boundary value problems for degenerate hyperbolic complex equations of first order in a simply connected domain, in which the boundary value problems include the Riemann-Hilbert problem and the Cauchy problem. We first give the representation of solutions of the boundary value problems for the equations, and then prove the uniqueness and existence of solutions for the problems. In [A.V. Bitsadze (1988). Some Classes of Partial Differential Equations . Gordon and Breach, New York; A.V. Bitsadze and A.N. Nakhushev (1972). Theory of degenerating hyperbolic equations. Dokl. Akad. Nauk, SSSR , 204 , 1289-1291 (Russian); M.H. Protter (1954). The Cauchy problem for a hyperbolic second order equation. Can. J. Math ., 6 , 542-553], the authors discussed some boundary value problems for hyperbolic equations of second order.     

GLOBAL SMOOTH SOLUTIONS OF DISSIPATIVE BOUNDARY VALUE PROBLEMS FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS

This paper discusses the following initial-boundary value problems for the first orderquasilinear hyperbolic systems:(u)/(t)+A(u)(u)/(x)=0,(1)u~Ⅱ=F(u~Ⅰ),as x=0,(2)u~Ⅰ=G(u~Ⅱ),as x=L,(3)u=u~0(x),as t=0,(4)where the boundary conditions(2),(3)satisfy F(0)=0,G(0)=0 and the dissipativeconditions,that is,the spectral radii of matrices B_1=(F)/(u~Ⅰ)(0)(G)/(u~Ⅱ)(0)and B_2(G)/(u~Ⅱ)(0)(F)/(u~Ⅰ)(0) are less than unit.Under certain assumptions it is proved that the initial-boundary problem (1)—(4)admits a unique global smooth solution u(x,t)and the C~1-norm丨u(t)丨σ~2of u(x,t)decaysexponentially to zero as t→∞,provided that the C~1-norm丨u~0丨σ~1of the initial data issufficiently small.     

On a Numerical Algorithm for Solving Boundary-Value Problems for Systems of Hyperbolic Equations of the First Order

In this article, we develop and substantiate a two-step, explicit–implicit numerical algorithm for solving boundary-value problems for systems of partial hyperbolic differential equations of the first order. The algorithm is based on finite-difference schemes with the differences taken against the flow. The approximation error of the solution has order two in the time variable and order one in the spatial variables.     

Boundary Value Problems for First Order Stochastic Differential Equations

In this paper, we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition （in the sense of expectation）. Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value. Then by using the contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the existence theorem. Finally, we explain our main results by an elementary example.     

一阶随机微分方程的边值问题

In this paper,we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition (in the sense of expectation).Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value.Then by using the contraction mapping principle and Leray-Schauder fixed point theorem,we obtain the existence theorem.Finally,we explain our main results by an elementary example.     

First Order LSFEM for Second Order Hyperbolic Problems

In the last years the interest in least squares finite element methods has grown due to some interesting properties of these methods (cf. the monographs [1], [2]). While for many elliptic problems the theoretical background has been established, only a few articles analyse least squares methods for transient problems. In this article some new stability estimates for the least squares method for the wave equation in 1 and 2 dimensions are derived. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Some Inverse Problems for First Order Operator-Differential Equations

Siberian Mathematical Journal - We study solvability of the inverse problems of recovering an unknown function on the nonlinear right-hand side of a first order operator-differential equation in...     

非线性Schr{odinger方程的初边值问题

本文证明了非线性Schrodinger方程的初值问题的H^S-解（1＜s≤2）的存在唯一性结果。