共查询到20条相似文献,搜索用时 93 毫秒
1.
In this paper,the higher order asymptotic behaviors of boundary blow-up solutions to the equation■in bounded smooth domain■are systematically investigated for p and q.The second and third order boundary behaviours of the equation are derived.The results show the role of the mean curvature of the boundary■and its gradient in the high order asymptotic expansions of the solutions. 相似文献
2.
V. S. Guliyev Zhijian Wu 《分析论及其应用》2005,21(2):143-156
We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included. 相似文献
3.
YAKUBOV Yakov 《中国科学 数学(英文版)》2013,56(1):105-122
This paper is a continuation of the author’s paper in 2009,where the abstract theory of fold completeness in Banach spaces has been presented.Using obtained there abstract results,we consider now very general boundary value problems for ODEs and PDEs which polynomially depend on the spectral parameter in both the equation and the boundary conditions.Moreover,equations and boundary conditions may contain abstract operators as well.So,we deal,generally,with integro-differential equations,functional-differential equations,nonlocal boundary conditions,multipoint boundary conditions,integro-differential boundary conditions.We prove n-fold completeness of a system of root functions of considered problems in the corresponding direct sum of Sobolev spaces in the Banach Lq-framework,in contrast to previously known results in the Hilbert L 2-framework.Some concrete mechanical problems are also presented. 相似文献
4.
The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel 1/sin 2(x-s) is discussed,and the main part of the asymptotic expansion of error function is obtained.Based on the main part of the asymptotic expansion,a series is constructed to approach the singular point.An extrapolation algorithm is presented and the convergence rate is proved.Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms. 相似文献
5.
By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results. 相似文献
6.
By topological degree theory,the three-point boundary value problem for p-Laplacian differential equation at resonance is studied. Some new results on the existence of solutions are obtained,which improve and extend some known ones in the previous literatures. 相似文献
7.
In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem. 相似文献
8.
In this paper, Hermitian positive definite solutions of the nonlinear matrix equation X + A^*X^-qA = Q (q≥1) are studied. Some new necessary and sufficient conditions for the existence of solutions are obtained. Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions, and the convergence analysis is also given. The theoretical results are illustrated by numerical examples. 相似文献
9.
BACKWARD ERROR ANALYSIS OF SYMPLECTIC INTEGRATORS FOR LINEAR SEPARABLE HAMILTONIAN SYSTEMS 总被引:3,自引:0,他引:3
PeterGrtz 《计算数学(英文版)》2002,(5)
Symplecticness, stability, and asymptotic properties of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nystrom methods applied to the simple Hamiltonian system p = -vg, q = kp are studied. Some new results in connection with P-stability are presented. The main part is focused on backward error analysis. The numerical solution produced by a symplectic method with an appropriate stepsize is the exact solution of a perturbed Hamiltonian system at discrete points. This system is studied in detail and new results are derived. Numerical examples are presented. 相似文献
10.
Gao Jia Xiao-ping Yang 《应用数学学报(英文版)》2006,22(4):589-598
Let Ωbelong to R^m (m≥ 2) be a bounded domain with piecewise smooth and Lipschitz boundary δΩ Let t and r be two nonnegative integers with t ≥ r + 1. In this paper, we consider the variable-coefficient eigenvalue problems with uniformly elliptic differential operators on the left-hand side and (-Δ)^T on the right-hand side. Some upper bounds of the arbitrary eigenvalue are obtained, and several known results are generalized. 相似文献
11.
J. A. Thas 《Designs, Codes and Cryptography》1996,9(1):95-104
Some recent results on k-arcs and hyperovals of PG(2,q),on partial flocks and flocks of quadratic cones of PG(3,q),and on line spreads in PG(3,q) are surveyed. Also,there is an appendix on how to use Veronese varieties as toolsin proving theorems. 相似文献
12.
A nonlinear spectral problem for a Sturm-Liouville equation-(p(x, λ)y'(x, λ))' + q(x, λ) y(x, λ) = 0 on a finite interval [a, b] with λ-dependent boundary conditions is considered. The spectral parameter λ is varying in an interval ∧ and p(x, λ), q(x, A) are real, continuous functions on [a, b] × ∧ Some criteria to the eigenvalue accumulation at the endpoints of A will be established. The results are applied to concrete problems arising in magnetohydrodynamics. 相似文献
13.
We prove some extension theorems for analytic objects, in particular sections of a coherent sheaf, defined in semi q-coronae of a complex space. Semi q-coronae are domains whose boundary is the union of a Levi flat part, a q-pseudoconvex part and a q-pseudoconcave part. Such results are obtained mainly using cohomological techniques. 相似文献
14.
A. A. Arkhipova 《Journal of Mathematical Sciences》2003,115(6):2735-2746
Nonlinear elliptic systems with q-growth are considered. It is assumed that additional nonlinear terms of the systems have q-growth in the gradient, q < 2. For Dirichlet and Neumann boundary-value problems we study the regularity of weak bounded solutions in the vicinity of the boundary. In the case of small dimensions (n q + 2), the Hölder continuity or partial Hölder continuity up to the boundary is proved for the solutions considered. In the previous article, the author studied the same problem for q = 2. Bibliography: 12 titles. 相似文献
15.
Tian Liang Tu 《数学学报(英文版)》2002,18(4):631-646
Let D be a smooth domain in the complex plane. In D consider the simultaneous approximation to a function and its ith (0 ≤i≤q) derivatives by Hermite interpolation. The orders of uniform approximation and approximation in the mean, are obtained under
some domain boundary conditions. Some known results are included as particular cases of the theorems of this paper.
Received May 25, 2000, Revised November 3, 2000, Accepted December 7, 2000 相似文献
16.
We recently proposed in [Cheng, XL et al. A novel coupled complex boundary method for inverse source problems Inverse Problem 2014 30 055002] a coupled complex boundary method (CCBM) for inverse source problems. In this paper, we apply the CCBM to inverse conductivity problems (ICPs) with one measurement. In the ICP, the diffusion coefficient q is to be determined from both Dirichlet and Neumann boundary data. With the CCBM, q is sought such that the imaginary part of the solution of a forward Robin boundary value problem vanishes in the problem domain. This brings in advantages on robustness and computation in reconstruction. Based on the complex forward problem, the Tikhonov regularization is used for a stable reconstruction. Some theoretical analysis is given on the optimization models. Several numerical examples are provided to show the feasibility and usefulness of the CCBM for the ICP. It is illustrated that as long as all the subdomains share some portion of the boundary, our CCBM-based Tikhonov regularization method can reconstruct the diffusion parameters stably and effectively. 相似文献
17.
Mathieu Dutour Sikiri Michel Deza Mikhail Shtogrin 《Discrete Applied Mathematics》2008,156(9):1518-1535
We consider here (p,s)-polycycles (3ps) i.e. plane graphs, such that all interior faces are p-gons, all interior vertices are s-valent and any vertex of the boundary (i.e. the exterior face) has valency within [2,s]. The boundary sequence of a (p,s)-polycycle P is the sequence b(P) enumerating, up to a cyclic shift or reversal, the consecutive valencies of vertices of the boundary. We show that the values p=3,4 are the only ones, such that the boundary sequence defines its (p,3)-filling (i.e. a (p,3)-polycycle with given boundary) uniquely.Also we give new results in the enumeration of maps Mn(p,q) (i.e. plane 3-valent maps with only p- and q-gonal faces, such that the q-gons are organized in an n-ring) and two of their generalizations.Both problems are similar (3-valent filling by p-gons of a boundary or of a ring of q-gons) and the same programs were used for both computations. 相似文献
18.
We extend a result of Pe?czyński showing that {?p(?q): 1 ≤ p, q ≤ ∞} is a family of mutually non isomorphic Banach spaces. Some results on complemented subspaces of ?p(?q) are also given. 相似文献
19.
For the two versions of the KdV equation on the positive half-line an initial-boundary value problem is well posed if one
prescribes an initial condition plus either one boundary condition if q
t
and q
xxx
have the same sign (KdVI) or two boundary conditions if q
t
and q
xxx
have opposite sign (KdVII). Constructing the generalized Dirichlet to Neumann map for the above problems means characterizing
the unknown boundary values in terms of the given initial and boundary conditions. For example, if {q(x,0),q(0,t)} and {q(x,0),q(0,t),q
x
(0,t)} are given for the KdVI and KdVII equations, respectively, then one must construct the unknown boundary values {q
x
(0,t),q
xx
(0,t)} and {q
xx
(0,t)}, respectively. We show that this can be achieved without solving for q(x,t) by analysing a certain “global relation” which couples the given initial and boundary conditions with the unknown boundary
values, as well as with the function Φ
(t)(t,k), where Φ
(t) satisfies the t-part of the associated Lax pair evaluated at x=0. The analysis of the global relation requires the construction of the so-called Gelfand–Levitan–Marchenko triangular representation
for Φ
(t). In spite of the efforts of several investigators, this problem has remained open. In this paper, we construct the representation
for Φ
(t) for the first time and then, by employing this representation, we solve explicitly the global relation for the unknown boundary values in terms of the given initial and boundary conditions and the function
Φ
(t). This yields the unknown boundary values in terms of a nonlinear Volterra integral equation. We also discuss the implications
of this result for the analysis of the long t-asymptotics, as well as for the numerical integration of the KdV equation. 相似文献
20.
Yasser Khalili Nematollah Kadkhoda Dumitru Baleanu 《Mathematical Methods in the Applied Sciences》2020,43(12):7143-7151
In the present work, we consider the inverse problem for the impulsive Sturm–Liouville equations with eigenparameter-dependent boundary conditions on the whole interval (0,π) from interior spectral data. We prove two uniqueness theorems on the potential q(x) and boundary conditions for the interior inverse problem, and using the Weyl function technique, we show that if coefficients of the first boundary condition, that is, h1,h2, are known, then the potential function q(x) and coefficients of the second boundary condition, that is, H1,H2, are uniquely determined by information about the eigenfunctions at the midpoint of the interval and one spectrum or partial information on the eigenfunctions at some internal points and some of two spectra. 相似文献