共查询到18条相似文献,搜索用时 92 毫秒
1.
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
2.
This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved. 相似文献
3.
In order to construct global solutions to two-dimensional(2 D for short)Riemann problems for nonlinear hyperbolic systems of conservation laws,it is important to study various types of wave interactions.This paper deals with two types of wave interactions for a 2 D nonlinear wave system with a nonconvex equation of state:Rarefaction wave interaction and shock-rarefaction composite wave interaction.In order to construct solutions to these wave interactions,the authors consider two types of Goursat problems,including standard Goursat problem and discontinuous Goursat problem,for a 2 D selfsimilar nonlinear wave system.Global classical solutions to these Goursat problems are obtained by the method of characteristics.The solutions constructed in the paper may be used as building blocks of solutions of 2 D Riemann problems. 相似文献
4.
赵增勤 《数学物理学报(B辑英文版)》2011,31(4):1569-1582
This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems. 相似文献
5.
YU Jianshe & GUO Zhiming College of Mathematics Information Sciences Guangzhou University Guangzhou China 《中国科学A辑(英文版)》2006,49(10):1303-1314
By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established. 相似文献
6.
丁协平 《数学物理学报(B辑英文版)》2011,31(3):1142-1154
In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces. 相似文献
7.
In this paper, the problems of the nonlocal initial conditions for the singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solutions for the initial boundary value problems are studied. 相似文献
8.
ZHANG Han-lin 《数学季刊》2005,20(4):385-389
A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems are studied, which reduced equations possess two intersecting solutions. 相似文献
9.
In this paper,we study the R m(m>0) Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(Vn,n).By using Plemelj formula,we get the solutions of R m(m>0) Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m(m>0) Riemann boundary value problems for harmonic functions and bi-harmonic functions. 相似文献
10.
The singularly perturbed generalized boundary value problems for semi-linear elliptic equations of fourth order are considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of generalized solutions for the boundary value problems are studied. 相似文献
11.
In this paper, we study the generalized vector equilibrium problems in real Hausdorff topological vector space settings. The concepts of weak solutions and strong solutions are introduced. Several new results of existence for the weak solutions and strong solutions of generalized vector equilibrium problems are derived. The new results extend and modify various existence theorems for similar problems. 相似文献
12.
A. M. Denisov 《Computational Mathematics and Mathematical Physics》2013,53(5):580-587
Two inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative are considered. The existence and uniqueness of their solutions are proved. As the small parameter tends to zero, the solutions of the inverse problems are proved to converge to solutions of inverse problems for a parabolic equation. 相似文献
13.
14.
Guochun Wen 《中国科学A辑(英文版)》1999,42(7):681-690
The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second
order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The
uniqueness theorem of solutions for the above problems and somea priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem,
the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding
theorems in literature.
Project supported by the National Natural Science Foundation of China (Grant No. 19671006). 相似文献
15.
In this paper, notions of global generalized solutions of Cauchy problems for the Hamilton–Jacobi–Bellman equation and for a quasilinear equation (a conservation law) are introduced in terms of characteristics of the Hamilton–Jacobi equation. Theorems on the existence and uniqueness of generalized solutions are proved. Representative formulas for generalized solutions are obtained and a relation between generalized solutions of the mentioned problems is justified. These results tie nonlinear scalar optimal control problems and one-dimensional stationary conservation laws. 相似文献
16.
高阶微分积分方程的单调迭代法及其应用 总被引:1,自引:0,他引:1
首先利用上下解方法以及微分不等式理论给出了n阶微分积分方程的初值问题解的存在性及其单调迭代法,然后将所得结果应用到n阶微分方程的两点边值问题,得到了n阶非线性两点边值问题解的存在性及其单调迭代法,所得结果推广了已有的结果. 相似文献
17.
反平面集中力作用下不同材料界面共线裂纹问题 总被引:4,自引:0,他引:4
本文研究在反平面集中力作用下,不同弹性材料界面上的共线裂纹问题.运用复变函数的解析延拓方法并结合对奇性主部的分析,获得了一般解;求出了几种典型情况的封闭解;算出了应力强度因子.本文解答的若干特殊情形,与前人成果吻合.通过比较,我们发现,在局部对称加载下,本文结果与同种材料的相应解答完全相同. 相似文献
18.
本文中,我们首先给出了一类混合似变分不等式问题.接着,在Banach空间中研究了它的解的存在性和唯一性.最后,讨论了混合似变分不等式问题的扰动问题,并证明了扰动问题的解的存在唯一性定理. 相似文献