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1.
In this paper we present some semismooth Newton methods for solving the semi-infinite programming problem. We first reformulate the equations and nonlinear complementarity conditions derived from the problem into a system of semismooth equations by using NCP functions. Under some conditions a solution of the system of semismooth equations is a solution of the problem. Then some semismooth Newton methods are proposed for solving this system of semismooth equations. These methods are globally and superlinearly convergent. Numerical results are also given. 相似文献
2.
考 虑具有未 知源项的 某些非 线性伪 抛物 型方程 的反演 问题. 首先 将伪抛 物型 方程初 边值问 题化为非线 性发展方 程 Couch y 问题,然 后,利用半 群理论,论 证发展 方程反问 题解的存 在唯一 性,最后, 利用不 动点方法得到 伪抛物型方程反 问题的可解性 相似文献
3.
M. D. Babych 《Ukrainian Mathematical Journal》1996,48(8):1141-1152
We present the theoretical justification and a method for practical realization of the process of separation of solutions isolated in a bounded domain for some classes of nonlinear integral equations. We study the problem of construction of a sequence of approximation equations by the method of mechanical quadratures and the problem of existence of solutions of these equations. We also present methods for approximate solution of these equations and obtaina posteriori error estimates. 相似文献
4.
In this note, we establish some local and global existence results for the Cauchy problem of a class of nonlinear dispersive equations which generalize the nonlinear Schrödinger equations and the Davey–Stewartson equations. These results improve some previously obtained results by some other authors when they are restricted to certain special equations. 相似文献
5.
求解非线性方程组的连续极小化方法 总被引:4,自引:0,他引:4
1.引言 求非线性方程组 F(x)=0 (1)(F:D?R~n→R~n)的各种方法中,牛顿法最为基本.但它只有局部收敛性和半局部收敛性,而且要求DF(x)~(-1)存在.为了扩大收敛范围及克服DF(x)奇异性带来的困难,用“连续化”的思想求方程(1)的解是一个有效的途径.这方面,已有许多工作,如[3—6].本文利用常微分方程几何理论,对连续化方法进行 些探讨,给出了沿积分曲线极小化求非线性方程组(1)的解的方法.考虑如下给定函数: 相似文献
6.
We consider the Cauchy problem for a class of nonlinear systems of differential equations of large dimension, establish some
properties of solutions, and prove that for a sufficiently large number of differential equations the last component of the
solution is an approximate solution to the initial value problem for a delay differential equation. 相似文献
7.
《复变函数与椭圆型方程》2012,57(4):257-270
In [], the authors discussed the Tricomi problem of second order mixed equations with nonsmooth degenerate line, but they only consider some special mixed equations. In [], the author discussed the uniqueness of solutions of the Tricomi problem for some second order mixed equations with nonsmooth degenerate line. The present article deals with oblique derivative problems for general second order mixed equations with nonsmooth parabolic degenerate line, and prove the uniqueness of solutions of the problems. We first give the formulation of the problems for the equations, and then prove the uniqueness of solutions for the above problems. 相似文献
8.
Su-rong Lin 《应用数学学报(英文版)》2010,26(2):267-276
The singularly perturbed boundary value problem of scalar integro-differential equations has been studied extensively by the differential inequality method . However, it does not seem possible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore , for n-dimensional vector integro-differential equations the problem has not been solved fully. Here, we study this nonlinear vector problem and obtain some results. The approach in this paper is to transform the appropriate integro-differential equations into a canonical or diagonalized system of two first-order equations. 相似文献
9.
We consider a general self-adjoint spectral problem, nonlinear with respect to the spectral parameter, for linear differential-algebraic
systems of equations. Under some assumptions, we present a method for reducing such a problem to a general self-adjoint nonlinear
spectral problem for a system of differential equations. In turn, this permits one to pass to a problem for a Hamiltonian
system of ordinary differential equations. In particular, in this way, one can obtain a method for computing the number of
eigenvalues of the original problem lying in a given range of the spectral parameter. 相似文献
10.
Grigory Panasenko 《Applicable analysis》2017,96(16):2771-2779
Method of asymptotic partial decomposition of a domain (MAPDD) proposed and justified earlier for thin domains (rod structures, tube structures) is generalized and justified for the multistructures, i.e. domains consisting of a set of thin cylinders connecting some massive 3D domains. In the present paper, the Dirichlet boundary value problem for the steady-state Stokes equations is considered. This problem is reduced to the Stokes equations in the massive domains coupled with the Poiseuille-type flows within the thin cylinders at some distance from the bases (the MAPDD approximation problem). The high-order estimates for the difference of the exact solution to the initial problem and the solution to the MAPDD approximation problem is proved. 相似文献
11.
吴霜 《数学年刊A辑(中文版)》2021,42(1):75-88
作者研究了一个条件平均场随机微分方程的最优控制问题.这种方程和某些部分信息下的随机最优控制问题有关,并且可以看做是平均场随机微分方程的推广.作者以庞特里雅金最大值原理的形式给出最优控制满足的必要和充分条件.此外,文中给出一个线性二次最优控制问题来说明理论结果的应用. 相似文献
12.
V. B. Levenshtam 《Journal of Mathematical Sciences》2009,163(1):89-110
A complete asymptotic expansion is constructed for solutions of the Cauchy problem for nth order linear ordinary differential
equations with rapidly oscillating coefficients, some of which may be proportional to ω
n/2, where ω is oscillation frequency. A similar problem is solved for a class of systems of n linear first-order ordinary differential
equations with coefficients of the same type. Attention is also given to some classes of first-order nonlinear equations with
rapidly oscillating terms proportional to powers ω
d
. For such equations with d ∈ (1/2, 1], conditions are found that allow for the construction (and strict justification) of the leading asymptotic term
and, in some cases, a complete asymptotic expansion of the solution of the Cauchy problem. 相似文献
13.
Andrzej Rozkosz 《Journal of Theoretical Probability》2013,26(4):1061-1083
We consider the Cauchy problem for systems of viscous conservation laws. We obtain three different but related stochastic representations of weak solutions of the problem: in terms of solutions to systems of usual backward stochastic differential equations, in terms of solutions to some stochastic backward systems, and in terms of solutions to some forward-backward stochastic differential equations. 相似文献
14.
Michal Fec?kan JinRong Wang 《Communications in Nonlinear Science & Numerical Simulation》2012,17(7):3050-3060
This paper is motivated from some recent papers treating the problem of the existence of a solution for impulsive differential equations with fractional derivative. We firstly show that the formula of solutions in cited papers are incorrect. Secondly, we reconsider a class of impulsive fractional differential equations and introduce a correct formula of solutions for a impulsive Cauchy problem with Caputo fractional derivative. Further, some sufficient conditions for existence of the solutions are established by applying fixed point methods. Some examples are given to illustrate the results. 相似文献
15.
Tomasz Klimsiak 《Potential Analysis》2012,36(2):373-404
We prove that under natural assumptions on the data strong solutions in Sobolev spaces of semilinear parabolic equations in
divergence form involving measure on the right-hand side may be represented by solutions of some generalized backward stochastic
differential equations. As an application we provide stochastic representation of strong solutions of the obstacle problem
by means of solutions of some reflected backward stochastic differential equations. To prove the latter result we use a stochastic
homographic approximation for solutions of the reflected backward equation. The approximation may be viewed as a stochastic
analogue of the homographic approximation for solutions to the obstacle problem. 相似文献
16.
Many authors have discussed the Tricomi problem for some second order equations of mixed type, which has important applications in gas dynamics. In particular, Bers proposed the Tricomi problem for Chaplygin equations in multiply connected domains [L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958]. And Rassias proposed the exterior Tricomi problem for mixed equations in a doubly connected domain and proved the uniqueness of solutions for the problem [J.M. Rassias, Lecture Notes on Mixed Type Partial Differential Equations, World Scientific, Singapore, 1990]. In the present paper, we discuss the general Tricomi-Rassias problem for generalized Chaplygin equations. This is one general oblique derivative problem that includes the exterior Tricomi problem as a special case. We first give the representation of solutions of the general Tricomi-Rassias problem, and then prove the uniqueness and existence of solutions for the problem by a new method. In this paper, we shall also discuss another general oblique derivative problem for generalized Chaplygin equations. 相似文献
17.
In this paper the problem of exponential stability of the zero state equilibrium of a discrete-time time-varying linear equation
described by a sequence of linear positive operators acting on an ordered finite dimensional Hilbert space is investigated.
The class of linear equations considered in this paper contains as particular cases linear equations described by Lyapunov
operators or symmetric Stein operators as well as nonsymmetric Stein operators. Such equations occur in connection with the
problem of mean square exponential stability for a class of difference stochastic equations affected by independent random
perturbations and Markovian jumping as well us in connection with some iterative procedures which allow us to compute global
solutions of discrete time generalized symmetric or nonsymmetric Riccati equations.
The exponential stability is characterized in terms of the existence of some globally defined and bounded solutions of some
suitable backward affine equations (inequalities) or forward affine equations (inequalities). 相似文献
18.
19.
In this paper, we consider the boundary value problem with the shift for nonlinear uniformly elliptic equations of second order in a multiply connected domain. For this sake, we propose a modified boundary value problem for nonlinear elliptic systems of first order equations, and give a priori estimates of solutions for the modified boundary value problem. Afterwards we prove by using the Schauder fixedpoint theorem that this boundary value problem with some conditions has a solution. The result obtained is the generlization of the corresponding theorem on the Poincare boundary value problem. 相似文献
20.
Guo Chun Wen 《Mathematische Nachrichten》2008,281(7):1047-1062
In [1]–[6], the author posed and discussed the Tricomi problem of second order mixed equations, but he only consider some special mixed equations. In [3], the author discussed the uniqueness of solutions of the Tricomi problem for some second order mixed equation with nonsmooth degenerate line. The present paper deals with the Tricomi problem for general second order mixed equations with degenerate curve on the sides of an angle. I first give the formulation of the above problem, and then prove the solvability of the Tricomi problem for the mixed equations with degenerate curve on the sides of an angle, by using the existence of solutions of the mixed problem for the degenerate elliptic equations (see [11]). Here I mention that the used method in this paper is different to those in other papers or books, because I introduce the new notation (2.1) below, such that the second order equation of mixed type can be reduced to the first order complex equation of mixed type with singular coefficients, hence I can use the advantage of complex analytic method. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献