共查询到20条相似文献,搜索用时 15 毫秒
1.
闻国椿 《数学物理学报(B辑英文版)》2007,27(3):663-672
The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved. 相似文献
2.
Guo-chun WEN 《应用数学学报(英文版)》2015,31(1):31-42
This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed(elliptichyperbolic) complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of H¨older continuity of a singular double integer is very difficult and interesting as in this Section 4 below. 相似文献
3.
Guochun Wen 《分析论及其应用》2005,21(2):118-131
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order. 相似文献
4.
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
5.
WEN Guo-chun 《高校应用数学学报(英文版)》2013,28(2):127-137
In this article,we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order with the boundary conditions in a multiply connected unbounded domain D.The above boundary value problem will be called Problem P.Under certain conditions,by using the priori estimates of solutions and Leray-Schauder fixed point theorem,we can obtain some results of the solvability for the above boundary value problem(0.1) and(0.2). 相似文献
6.
Gen-sun FANG & Li-xin QIAN School of Mathematical Sciences Beijing Normal University Beijing China College of Mathematics Physics Zhejiang Normal University Jinhua China 《中国科学A辑(英文版)》2007,50(1):100-104
In this paper, we introduce a problem of the optimization of approximate solutions of operator equations in the probabilistic case setting, and prove a general result which connects the relation between the optimal approximation order of operator equations with the asymptotic order of the probabilistic width. Moreover, using this result, we determine the exact orders on the optimal approximate solutions of multivariate Preldholm integral equations of the second kind with the kernels belonging to the multivariate Sobolev class with the mixed derivative in the probabilistic case setting. 相似文献
7.
In an earlier paper, we proved the existence of solutions to the Skorohod problem with oblique reflection in time-dependent domains and, subsequently, applied this result to the problem of constructing solutions, in time-dependent domains, to stochastic differential equations with oblique reflection. In this paper we use these results to construct weak approximations of solutions to stochastic differential equations with oblique reflection, in time-dependent domains in Rd, by means of a projected Euler scheme. We prove that the constructed method has, as is the case for normal reflection and time-independent domains, an order of convergence equal to 1/2 and we evaluate the method empirically by means of two numerical examples. Furthermore, using a well-known extension of the Feynman-Kac formula, to stochastic differential equations with reflection, our method gives, in addition, a Monte Carlo method for solving second order parabolic partial differential equations with Robin boundary conditions in time-dependent domains. 相似文献
8.
9.
Xu-Jia WANG 《数学年刊B辑(英文版)》2006,27(2):169-178
In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive. 相似文献
10.
闻国椿 《数学年刊B辑(英文版)》1983,(1)
In this paper,we discuss the third boundary elliptic systems of second order(1.1)in a multiplyconnceted domain.We first prove that problem III of the harmonic function has a unique solutionand estabilish the integral expression of solutions for problem III of the systems(1.1).Next,usingthe above results,a priori estimates for solutions of problem Ill of the systems(1.1)and Leray-Schauder theorem,we obtain the result on the solvability of problem III for the nonlitnear systems(1.1)satisfying some conditions. 相似文献
11.
RUZIEV M. Kh 《偏微分方程(英文版)》2014,(2):176-188
In this paper, we study the boundary-value problem for mixed type equation with singular coefficient. We prove the unique solvability of the mentioned problem with the help of the extremum principle. The proof of the existence is based on the theory of singular integral equations, Wiener-Hopf equations and Fredholm integral equations. 相似文献
12.
Guo Chun Wen 《数学学报(英文版)》2008,24(11):1759-1774
The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains. 相似文献
13.
Jinjun Fan Fangfang Han 《Annals of Differential Equations》2014,(3):282-290
In this paper, we consider the existence of positive solutions to a three-point boundary value problem for second order dynamic equations with derivative on time scales.Applying Leggett-Williams fixed point theorem, we obtain at least three positive solutions to the problem. An example is also presented to illustrate the applications of the results obtained. 相似文献
14.
In this paper,we study the initial-boundary value problem for a class of singular parabolic equations.Under some conditions,we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method.As a byproduct,we prove the existence of solutions to some problems with gradient terms,which blow up on the boundary. 相似文献
15.
In this paper,we will discuss smoothness of weak solutions for the system of second orderdifferential equations eith non-negative characteristies.First of all,we establish boundary,and interiorestimates and then we prove that solutions of regularization problem satisfy Lipschitz condition. 相似文献
16.
In this paper, we discuss the existence of weak solutions to the initial and boundary value problem of a class of nonlinear degenerate parabolic equations in non-divergence form. Applying the method of parabolic regularization, we prove the existence of weak solutions to the problem. By carefully analyzing the approximate solutions to the problem, we make a series of estimates to the solutions and prove the weak convergence of the approximation solution sequence. Finally we testify the existence of weak solutions to the problem. 相似文献
17.
In this paper,we discuss a class of the quasillinear hyperbolic equations with the inhomogeneous terms:ur σ(v)x 2α(t)u=0,vr-ux=0 Under the certain of hypothesis,we prove the globally existence theorems of the smooth solutions for is cauchy problem. 相似文献
18.
In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary. 相似文献
19.
《数学研究与评论》1984,(3)
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 Poincar boundary value problem. 相似文献
20.
ZhangWenling 《偏微分方程(英文版)》2004,17(4):316-328
In this paper, we consider the Cauchy problem for some dispersive equations. By means of nonlinear estimate in Besov spaces and fixed point theory, we prove the global well-posedness of the above problem. What‘s more, we improve the scattering result obtained in [1]. 相似文献