两参数非线性椭圆型方程的激波渐近解（英文）

本文讨论一类两参数非线性椭圆型方程边值问题.得到原问题的外部解,引入伸长变量和在边界和外部解的内部间断点附近设置局部坐标系,构造边界层和内部层校正项.在适当的条件下,利用微分不等式,证明边值问题激波解的存在性并研究解的渐近性态.     

一具有阻尼非线性双曲型方程初边值问题整体解的不存在性

本文证明一具有阻尼非线性双曲型方程初边值问题局部广义解的存在性和唯一性,并给出此问题解爆破的充分条件.     

一阶带间断系统的椭圆型复方程的Hilbert边值问题

本文研究一阶带间断系数的椭圆型复方程的Ｈｉｂｅｒｔ边值问题，在一定条件下给出了上述问题解的存在性，可解条件以及解的积分表示式。     

二阶拟线性混合(椭圆一双曲)型方程的Frankl问题

本文证明了一类二阶拟线性混合型方程Frankl边值问题解的唯一性与存在性.文中先给出解的一种表示式,据此证明边值问题解的唯一性.进而求得解的估计式,据此再使用复分析理论与"参数开拓法”证明了边值问题解的存在性.这里使用的方法有别于其他作者对混合型方程通常使用的积分方程方法.     

一类拟线性抛物型方程间断初边值问题

本文我们将讨论拟线性抛物型方程具间断数据的初边值问题（１）－（３）．在某些条件下，我们将证明问题的有界解的存在、唯一性及解在间断点处的性态．     

二阶拟线性混合（椭圆—双曲）型方程的Frankl问题

本文证明了一类二阶阶拟线性混合型方程Frankl边值问题解的唯一性与存在性,文中先给出解后一种表示式,据此证明边值问题解的唯一性,进而求得解的估计式,据此再使用复分析理论与“参数开拓法”证明了边值问题解的存在性,这里使用的方法有别于其他作者对混合型方程通常使用的积分方程方法。     

关于猝灭问题的一些结果及其应用

本文研究一类含奇异项的半线性抛物方程的初边值问题,给出了该问题的古典解整体存在或发生猝灭现象的判据以及猝灭解的生命跨度估计。同时,还用上述结果研究了一类含超Sobolev临界指标的半线性椭圆方程的Dirichlet边值问题,获得了正解的存在性结果。     

人口问题中的三维Ginzburg-Landau模型方程的Cauchy问题

本文证明人口问题中的三维Ginzburg－Landau模型方程的周期边值问题和Cauchy问题的广义解和古典解的整体存在性、唯一性以及解的渐进性质．     

The Hilbert Problem for the First Order Elliptic Complex Equation With Discontinuous Coefficients

本文研究一阶带间断系数的椭圆型复方程的Ｈｉｌｂｅｒｔ边值问题，在一定条件下给出了上述问题解的存在性、可解条件以及解的积分表示式．     

一阶混合型方程组的间断边值问题

本文论讨单连通区域上一阶线性混合型(椭圆—双曲型)方程组的间断边值问题.我们首先给出混合型方程组特别是最简单的混合型方程组解的表示式,然后使用逐次逼近法,证明上述边值问题解的存在性与唯一性.由以上结果,可导出A.V.Bitsadze所得的Lavrent’ev-Bitsadze方程u     

Discontinuous Oblique Derivative Problem for Second Order Equations of Mixed Type in General Domains

In [L. Bers (1958). Mathematical Aspects of Subsonic and Transonic Gas Dynamics . Wiley, New York; A.V. Bitsadze (1988). Some Classes of Partial Differential Equations . Gordon and Breach, New York; J.M. Rassias (1990). Lecture Notes on Mixed Type Partial Differential Equations. World Scientific, Singapore; H.S. Sun (1992). Tricomi problem for nonlinear equation of mixed type. Sci. in China ( Series A ), 35 , 14-20], the authors proposed and discussed the Tricomi problem of second order equations of mixed type in a special domain, and in [G.C. Wen (1998). Oblique derivative problems for linear mixed equations of second order. Sci. in China ( Series A ), 41 , 346-356], the author discussed the oblique derivative problem of second order equations of mixed type in a special domain. The present article deals with the discontinuous oblique derivative problem for quasilinear second order equations of mixed (elliptic-hyperbolic) type in general domains. Firstly, we give the formulation of the above boundary value problem, and then prove the existence of solutions for the above problem in general domains, in which the complex analytic method is used.     

Oblique derivative problems for second order nonlinear equations of mixed type with degenerate hyperbolic curve

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.     

Oblique Derivative Problem for Quasilinear Mixed (Lavrentév-Bitsadze) Equations of Second Order in Two Connected Domains

In this article, we first give the representation of solutions for the oblique derivative problem of mixed (Lavrentév-Bitsadze) equations in two connected domains, afterwards prove the uniqueness of solutions of the above problem. Moreover, we prove the solvability of oblique derivative problem for quasilinear mixed (Lavrentév-Bitsadze) equations of second order, and obtain a priori estimates of solutions of the above problem. The above problem is an open problem proposed by Rassias.     

Uniqueness of Oblique Derivative Problems for Second Order Equations of Mixed Type with Nonsmooth Degenerate Line

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.     

Oblique derivative problems for second order nonlinear equations of mixed type in multiply connected domains

In this paper, the unique solvability of oblique derivative boundary value problems for second order nonlinear equations of mixed (elliptic-hyperbolic) type in multiply connected domains is proved, which mainly is based on the representation of solutions for the above boundary value problem, and the uniqueness and existence of solutions of the above problem for the equation u_xx + sgn y u_yy = 0.     

AN IRREGULAR OBLIQUE DERIVATIVE PROBLEM FOR SOME NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER

1FormulationofirregularObliqueDerivativeProblemLetDbean(N 1)-connecteddomainwithboundaryr=UU=,r,6Cj(0相似文献   

OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE

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.     

Estimates of solutions of initial-irregular oblique derivative problems for fully nonlinear parabolic equations

In this paper the initial-irregular oblique derivative problems for fully nonlinear parabolic equations of second order are proposed, and then some a priori estimates of solutions for the above problems are given.     

SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

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.