共查询到19条相似文献,搜索用时 93 毫秒
1.
对于给出的一类二阶线性双曲型方程,通过未知变量替换,将其化为一阶对称双曲型方程组.可以证明这个一阶对称双曲型方程组与原来的二阶线性双曲型方程的Cauchy问题的经典解在某种意义下是等价的. 相似文献
2.
3维双曲空间中曲面的双曲Gauss映照和法Gauss映照 总被引:3,自引:0,他引:3
本文导出了3维双曲空间中曲面的双曲Gauss映照和法Gauss映照的关系,发现了一般的曲面由双曲Gauss映照和平均曲率函数唯一确定,并证明了双曲Gauss映照所满足的二阶线性椭圆方程,给出了两种形式的关于双曲Gauss映照的三阶非线性偏微分方程(组)的一个解. 相似文献
3.
双曲-双曲奇异摄动混合问题的一致收敛格式 总被引:1,自引:0,他引:1
本文构造了二阶双曲-双曲奇异摄动混合问题的差分格式,给出了差分解的能量不等式,并证明了差分解在离散范数下关于小参数一致收敛于摄动问题的解. 相似文献
4.
一类非线性双曲型方程的广义Galerkin方法 总被引:4,自引:1,他引:3
本文研究一类非线性双曲型方程混合问题的广义Galerkin方法,即广义差分法.本文应用分片线性试探函数空间和分片常数检验函数空间,讨论了非线性二维二阶双曲型问题半离散和全离散方程的收敛性和稳定性,得到了与线性有限元方法相同的最优收敛阶. 相似文献
5.
6.
在初始版本的第一,二Bianchi恒等式的基础上,利用二阶或三阶协变导数引申出扩展的二阶协变和三阶协变Bianchi恒等式.这类二阶协变Bianchi恒等式在黎曼曲率张量沿着两类特殊的几何流-里奇(Ricci)流和双曲几何流的演化方程中有一定的应用.给出这方面的应用例子并加以阐述. 相似文献
7.
该文利用复分析的方法对双曲区域实施共形映照,通过将双曲区域的边界曲线变换为直线段,研究了另一类更一般区域上的拟线性二阶混合型方程的不连续边值问题,得到了一些较新的可解性结果的推广. 相似文献
8.
本文在[5]的基础上,讨论了二阶完全非线性严格双曲方程的两个具有限高阶相切的余法波的干扰问题. 相似文献
9.
本文利用Carleman估计和算子链方法,研究了一类初始曲线含重特征点的二阶退缩双曲型方程的柯西问题在分布类中的唯一性. 相似文献
10.
二阶退化双曲型方程的Darboux型问题 总被引:1,自引:0,他引:1
本文讨论二阶退化双曲型方程的一些边值问题.文中先给出第一Darboux问题和一般斜微商边值问题的提法和解的表示式,然后使用复分析方法证明了上述问题解的存在唯一性. 相似文献
11.
Guo Chun Wen 《数学学报(英文版)》2011,27(10):2051-2064
The present paper deals with oblique derivative problems for second order nonlinear equations of mixed type with degenerate
hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations
is given, next the representation and estimates of solutions for the above problems are obtained, finally the existence of
solutions for the problems is proved by the successive iteration of solutions of the equations and the fixed-point principle.
In this paper, we use the complex analytic method, namely the new partial derivative notations, elliptic complex functions
in the elliptic domain and hyperbolic complex functions in the hyperbolic domain are introduced, such that the second order
equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients,
and then the advantage of complex analytic method can be applied. 相似文献
12.
《复变函数与椭圆型方程》2012,57(9):839-851
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. 相似文献
13.
A. I. Kozhanov 《Journal of Mathematical Sciences》2011,173(2):207-220
This paper presents results on the solvability in classes of regular solutions of some boundary-value problems with Bitsadze?CSamarskii condition for one-dimensional hyperbolic equations of the second order. 相似文献
14.
Some three-dimensional (3D) problems for mixed type equations of first and second kind are studied. For equation of Tricomi
type, they are 3D analogs of the Darboux (or Cauchy-Goursat) plane problem. Such type problems for a class of hyperbolic and
weakly hyperbolic equations as well as for some hyperbolic-elliptic equations are formulated by M. Protter in 1952. In contrast
to the well-posedness of the Darboux problem in the 2D case, the new 3D problems are strongly ill-posed. A similar statement
of 3D problem for Keldysh-type equations is also given. For mixed type equations of Tricomi and Keldysh type, we introduce
the notion of generalized or quasi-regular solutions and find sufficient conditions for the uniqueness of such solutions to
the Protter’s problems. The dependence of lower order terms is also studied. 相似文献
15.
In this paper,we consider the singular boundary value problems for second order quasilinear ordinary differential equations and prove existence and convergence on second order perturbation terms.The result is applied to solve the Riemann problem for 2×2 hyperbolic conservation laws,which is a partial differential equation arising in applied mathematical area. 相似文献
16.
Dong-Gun Park Jin-Mun Jeong Han-Geul Kim 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):235-253
In this paper we establish the wellposedness and regularity properties of solutions of Cauchy problems for semilinear hyperbolic
equations of second order with unbounded principal operators. An example illustrating how our results apply is given.
相似文献
17.
We consider an abstract Cauchy problem for a system of nonhomogeneous abstract differential equations in Hilbert spaces. The
“main” equation is of the second order and “boundary” equations are of the first order. Existence of a solution is proved.
Application to mixed (initial boundary-value) problems for one-dimensional second order hyperbolic equations and for fourth
order PDEs with the time derivative in boundary conditions has been shown.
The first author was partially supported by 60% funds of the University of Bologna and G.N.A.M.P.A. of INdAM; the second author
was supported by the Israel Ministry of Absorption. 相似文献
18.
OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE 总被引:1,自引:0,他引:1
闻国棒 《数学物理学报(B辑英文版)》2008,28(3):604-612
The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. 相似文献
19.
On one approach to a posteriori error estimates for evolution problems solved by the method of lines 总被引:2,自引:0,他引:2
Summary. In this paper, we describe a new technique for a posteriori error estimates suitable to parabolic and hyperbolic equations
solved by the method of lines. One of our goals is to apply known estimates derived for elliptic problems to evolution equations.
We apply the new technique to three distinct problems: a general nonlinear parabolic problem with a strongly monotonic elliptic
operator, a linear nonstationary convection-diffusion problem, and a linear second order hyperbolic problem. The error is
measured with the aid of the -norm in the space-time cylinder combined with a special time-weighted energy norm. Theory as well as computational results
are presented.
Received September 2, 1999 / Revised version received March 6, 2000 / Published online March 20, 2001 相似文献