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1.
INTERFACEPROBLEMSFORELLIPTICDIFFERENTIALEQUATIONSYINGLUNGANAbstractAnewapproachisgiventoanalysetheregularityofsolutionsnears...  相似文献   

2.
This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H2 when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H2, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

3.
We study the structure of solutions to the interface problems for second order quasi-linear elliptic partial differential equations in two dimensional space. We prove that each weak solution can be decomposed into two parts near singular points, a finite sum of functions in the form of cr^α log^m rφ(θ) and a regular one w. The coefficients c and the C^{1,α} norm of w depend on the H¹-norm and the C^{º, α}-norm of the solution, and the equation only.  相似文献   

4.
Summary The method based upon a constructive reduction of coercive singular perturbations to regular ones, introduced in 1977 (see [4]) and developed later on (see [9–11]) is applied for computing the asymptotic expansions for eigenvalues of coercive singular perturbations, when the small parameter goes to zero. The same method turns out to be useful for investigating the asymptotic behaviour of solutions to quasi-linear coercive singular perturbations in the neighbourhood of the bifurcation points. It can be applied to classes of quasi-linear singular perturbations whose principal linear part in local representation is coercive and the nonlinear part is analytic in some ball in the solution space with values in the data space. The results are summarized in [7, 8].  相似文献   

5.
The author proposes a two-dimensional generalization of Constantin-Lax-Majda model. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line (vorticity formulation), the author presents some further model equations. He possibly models various aspects of difficulties related with the singular solutions of the Euler and Navier-Stokes equations. Some discussions on the possible connection between turbulence and the singular solutions of the Navier-Stokes equations are made.  相似文献   

6.
We are concerned with the qualitative analysis of positive singular solutions with blow-up boundary for a class of logistic-type equations with slow diffusion and variable potential. We establish the exact blow-up rate of solutions near the boundary in terms of Karamata regular variation theory. This enables us to deduce the uniqueness of the singular solution.  相似文献   

7.
SingularPointsNearanX_0-breakingDoubleSingularFoldPointinZ_2-symmetricNonlinearEquationsSuYi(苏毅)andWuwei(吴微)(DepartmentofMathe...  相似文献   

8.
粒子的相互作用、极限环和相变   总被引:6,自引:0,他引:6  
从各种相互作用的规范理论出发,讨论了规范场方程的某些新的解,并引入了势,然后探讨了它们与极限环、各种奇异点的关系,最后论述了这些结果可能具有的粒子性质和相变等物理意义.  相似文献   

9.
该文利用不动点指数理论讨论了Banach空间中一类带奇异性的脉冲微分方程Neumann边值问题多解的存在性,并给出了应用  相似文献   

10.
At the boundary of the class of Morse-Smale vector fields there are vector fields whose unique degenerate phenomena is a singular cycle. We first characterize and classify all singular cycles which contains only one degeneracy (thesimple singular cycles: ssc). Each of these cycles defines a condimension one submanifold of vector fields. For some ssc its codimension one submanifold is a regular part of the boundary of the Morse-Smale systems. We characterize those ssc that defines this type of submanifold. Our ambient space isn dimensional,n2.Supported by Fondecyt, Proyecto 1930863.  相似文献   

11.
利用锥拉伸及锥压缩不动点定理,研究了Banach空间中一类带奇异性的脉冲微分方程边值问题多个正解的存在性.  相似文献   

12.
We investigate well-posedness of initial-boundary value problems for a class of nonlinear parabolic equations with variable density. At some part of the boundary, called singular boundary, the density can either vanish or diverge or not need to have a limit. We provide simple conditions for uniqueness or non-uniqueness of bounded solutions, depending on the behaviour of the density near the singular boundary.  相似文献   

13.
We study the steady-state Maxwell equations in a non-smooth, non-convex, axially symmetric domain Ω. The solutions are written as the orthogonal sum of a regular part within H1 (Ω)3 and a singular part. We show that, like in the two-dimensional case, the singular part is related to the (axisymmetric) singular eigenfuctions of the Laplacian, and hence is of finité dimension.  相似文献   

14.
On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Hlder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Hlder continuous property on the boundary.  相似文献   

15.
郭林 《应用数学》2007,20(4):826-829
本文构造了一个新的正则锥,运用非紧减算子的不动点定理,得到了一类非线性奇异边值问题正解的唯一性,改进了有关结果.  相似文献   

16.
利用锥理论和M¨onch不动点定理,讨论了Banach空间中一类带奇异性的脉冲微分方程边值问题正解的存在性.作为其应用,给出了一个例子.  相似文献   

17.
This paper represents the third part of a contribution to the “dictionary” of homogeneous linear differential equations with polynomial coefficients on one hand and corresponding difference equations on the other. In the first part (cf. [4]) we studied the case that the differential equation (D) has at most regular singularities at O and at ∞, and arbitrary singularities in the rest of the complex plane. We constructed fundamental systems of solutions of a corresponding difference equation (A), using integral transforms of microsolutions of (D) at its singular points in ?. In the second part ([5]) we considered differential equations having at most a regular singularity at O and an irregular one at O. We used integral transforms of asymptotically flat solutions of (D) to define it fundamental system of solutions of (Δ), holomorphic in a right half plane, and integral transforms of sections of the sheaf of solutions of (D) modulo solutions with moderate growth as t → 0 in some sector, to define a fundamental system of (Δ), holomorphic in a left half plane. In this final part we combine the techniques and results of the preceding papers to deal with the general case.  相似文献   

18.
The local theory of singular points is extended to a large class of linear, second-order, ordinary differential equations which can be physical Schroedinger equations, or govern the modulation of real oscillators or waves. In addition to Langer's fractional turning points, such equations admit highly irregular points at which the coefficients of the differential equation can be almost arbitrarily multivalued. (Genuine coalescence of singular points, however, is not considered.) A local representation of the solutions is established, which generalizes Frobenius' method of power series, and reveals a remarkable, two-variable structure. Bounds are obtained on the departure of solution structure from the structure characteristic of regular points.  相似文献   

19.
一类四阶奇异半正Sturm-Liouville边值问题的正解   总被引:3,自引:0,他引:3  
在Sturm-Liouville边界条件下研究较广泛的一类四阶奇异半正微分方程,得到其C2[0,1]正解与C3[0,1]正解存在的新结果,并给出了其正解与该边值问题的格林函数之间的某些联系.  相似文献   

20.
An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces. This decomposition can be seen as an analog of the Lebesgue decomposition of a measure into a regular part and a singular part. The two parts of a relation are characterized metrically and in terms of Stone’s characteristic projection onto the closure of the linear relation.  相似文献   

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