THE INITIAL DIRICHLET BOUNDARY VALUE PROBLEM FOR GENERAL SECOND ORDER PARABOLIC SYSTEMS IN NONSMOOTH MANIFOLDS

Abstract

We consider some unilateral boundary value problems in polygonal and polyhedral domains with unilateral transmission conditions. Regularity results in terms of weighted Sobolev spaces are obtained using a penalization technique, similar regularity results for the penalized problems and by showing uniform estimates with respect to the penalization parameter.     

NUMERICAL RECONSTRUCTION OF INTERNAL STATES BY BOUNDARY MEASUREMENTS FOR THE LAPLACE EQUATION

The purpose of the paper is to present a unified numerical method for problems consisting of the conventional boundary value problem. Cauchy problem, under-determined problem, and over-determined problem. The method is based on the direct variational approach, which paraphrases the problems into the primary and adjoint boundary value problems that can be tackled by commonly used computer programs for the numerical solution of the Laplace equation.     

THE STABILITY OF A VARIATIONAL METHOD FOR THE SOLUTION OF A LINEAR HYPERBOLIC INITIAL BOUNDARY VALUE PROBLEM

Abstract

The numerical stability of a variational method that is used to obtain the solution of a one space dimension wave equation with initial and boundary conditions is analyzed. The phase speed and group velocity of the numerical solution are also investigated with respect to that of the exact solution.     

解一类半线性外边值问题的自然边界元与有限元耦合法

In this paper, we combine a finite element approach with the natural boundary element method to stduy the weak solvability and Galerkin approximations of a class of semilinear exterior boundary value problems. Our analysis is mainly based on the variational formulation with constraints. We discuss the error estimate of the finite element solution and obtain the asymptotic rate of convergence O（h^n) Finally, we also give two numerical examples.     

HILBERT SPACES ASSOCIATED WITH SECOND ORDER ELLIPTIC OPERATORS AND APPLICATIONS TO BOUNDARY VALUE PROBLEMS AND VARIATIONAL INEQUALITIES

Abstract

Boundary value problems and variational inequalities, associated with second order elliptic operators, will be studied in a Hilbert space framework. In this space, functions will have (at least) locally square integrable derivatives of order up to two. Also the conormal derivative, extended by continuity, will be square integrable on the boundary of the region considered. Criteria for approximating elements of the Hilbert space by smooth functions will be given and thus closed convex sets, associated with inequalities on the boundary, exist.

The idea of the present approach originated from the method suggested by Lions and Magenes, for putting some regular elliptic problems in the variational setting. The differential equation is multiplied by Qv, with Q some operator and v a function and the result is integrated as required.     

THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS

1.IntroductionManyproblemsarisinginfluidmechanicsaregiveninanunboundeddomain,suchasfluidflowaroundobstacles.Whencomputingthenumericalsolutionsoftheseproblems,oneoftenintroducesartificialboundariesandsetsupaxtificialboundaryconditionsonthem.Thentheoriginal…     

THE BOUNDARY VALUE PROBLEMS OF A CLASS OF ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT

The boundary value problems of a class of elliptic equation with a curveof turning point are considered. Using the method of multiple scales and thecomparison theorem, the asymptotic behavior of solution for the boundary valueproblem is studied.     

Problemi al contorno con condizioni omogenee per le equazioni quasi-ellittiche

Summary We are concerned with non-variational boundary value problems, with omogeneus boundary conditions, for linear partial differential equations of quasi-elliptic type in a bounded domain Θ in Rⁿ. It is well known that some of difficulties which arise in treating such problems, in comparison with ? regular ? elliptic problems, are connected with the presence of angular points in Θ: let us point out withB. Pini [32] that ? a bounded domain for which it is possible to assign a correct boundary value problem for a quasi-elliptic but not elliptic equation always has angular points ?. We suppose Θ is a cartesian product of a finite number of open sets and, in order to overcome the difficulties attached to the presence of angular points in Θ, taking as a model the two previous papers[33], [34] devoted to elliptic problems with singular data, we investigate the problem within suitable Sobolev weight spaces, connected with the angular points of Θ and included in the ones we have studied in[35]. Within such spaces we get existence and uniqueness theorems.

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Lavoro eseguito con contributo del C. N. R.

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Entrata in Redazione il 30 ottobre 1971.     

SELF-ADJOINTNESS IN THE WEYL LIMIT CASES. THE ROLE OF BOUNDARY CONDITIONS

ABSTRACT

The role of boundary conditions in assuring self-adjointness for the singular second order Sturm-Liouville operator -yⁿ + qy is discussed, both in the limit circle and limit point cases.     

一类非线性发展方程初边值问题解的Blow—up

本文利用Fourier变换方法,研究了一类非线性拟双曲方程的初边值问题的解的bolw-up问题,并给出了其解在有限时间内bolw-up的条件。     

Nonlinear Elliptic Equations with Mixed Singularities

We study non-variational degenerate elliptic equations with mixed singular structures, both at the set of critical points and on the ground touching points. No boundary data are imposed and singularities occur along an a priori unknown interior region. We prove that positive solutions have a universal modulus of continuity that does not depend on their infimum value. We further obtain sharp, quantitative regularity estimates for non-negative limiting solutions.     

带有p-Laplace算子的分数阶边值问题的特征区间

本文研究了一类带有p-Laplace算子的分数阶微分方程两点边值问题.利用锥上的不动点定理,得到了这类边值问题的特征区间,推广了整数阶边值问题情形的结论.     

THE BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS OFA BIHARMONIC BOUNDARY VALUE PROBLEM

1.IntroductionWeconsiderahomogeneousisotropicandlinearelasticKirchhoffplateunderlateralloaddistributedovertheplatefix[--t,t].ThedomainfiERZisboundedwiththesmoothboundaryr.Inthestaticequilibrium,weconsiderthefreetypeboundaryconditiononr.Thenthedeflectionusatisfiesthefollowingproblem:whereD~--E0h'.12(1--ac,isthebendingstiffnessoftheplatewithhbeingtheplatethicknessandEOandu(0相似文献   

一类奇异方程两点边值问题的差分—样条校正解

本文考虑一类奇异方程两点边值问题的差分解和样条数值解法,证明了差分解,样条解分别从两侧逼近精确解,从而得到高精度的差分-样条校正解. 考虑如下形式的奇异边值问题:     

MIXED BOUNDARY VALUE PROBLEM FOR SECOND－ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

（陈庆祥）ＭＩＸＥＤＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＦＯＲＳＥＣＯＮＤ－ＯＲＤＥＲＳＹＳＴＥＭＯＦＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＴＨＥＥＬＬＩＰＴＩＣＴＹＰＥ￥ＣｈｅｎＱｉｎｇｘｉａｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｚｈｏｎｇｓ...     

THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS

§ 1　 IntroductionA class of singularly perturbed boundary value problems were studied by Mo[1～ 6] .Now we consider the following singularly perturbed nonlinear boundary value problem ofthe formεd2 ydx2 =f(x,y,y′) ,　 0 相似文献   

椭圆问题的非线性边界条件均匀化

在本文我们讨论了在等值面边值问题中的非线性边界条件的均匀化,推广了相应的边界条件均匀化结果,而且可应用到用于处理热敏电阻问题中的一类非线性非局部边值问题的边界条件均匀化问题。     

NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH STRUM-LIOUVILLE BOUNDARY CONDITIONS

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.     

拟线性椭圆边值问题有限元校正方法

§1.主要结果 考虑拟线性椭圆边值问题 u=0,在?Ω上,其中Ω是R~2中凸多边形,z=(x,y),D_1=?/?x,D_2=?/?y,a_i(z,ξ_0,ξ_1,ξ_2)是定义在Ω×R×R×R上的函数,适当光滑,i=0,1,2.定义     

THE SYMMETRIC POSITIVE SOLUTIONS OF $2n$-ORDER BOUNDARY VALUE PROBLEMS ON TIME SCALES

In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle, the symmetric form of the Green''s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.