共查询到20条相似文献,搜索用时 0 毫秒
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In this paper we find conditions that guarantee that regular boundary value problems for elliptic differential-operator equations of the second order in an interval are coercive and Fredholm, and we prove the compactness of a resolvent. We apply this result to find some algebraic conditions that guarantee that regular boundary value problems for degenerate elliptic differential equations of the second order in cylindrical domains have the same properties. Note that considered boundary value conditions are nonlocal and are differential only in their principal part, and a domain is nonsmooth. 相似文献
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We propose and analyse a fully discrete PetrovGalerkinmethod with quadrature, for solving second-order, variable coefficient,elliptic boundary value problems on rectangular domains. Inour scheme, the trial space consists of C2 splines of degreer 3, the test space consists of C0 splines of degree r 2, and we use composite (r 1)-point Gauss quadrature.We show existence and uniqueness of the approximate solutionand establish optimal order error bounds in H2, H1 and L2 norms. 相似文献
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The method of fundamental solutions for elliptic boundary value problems 总被引:23,自引:0,他引:23
The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over
the last three decades. Several applications of MFS-type methods are presented. Techniques by which such methods are extended
to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are also outlined.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Susanne C. Brenner. 《Mathematics of Computation》2002,71(238):507-525
The multigrid -cycle algorithm using the Richardson relaxation scheme as the smoother is studied in this paper. For second-order elliptic boundary value problems, the contraction number of the -cycle algorithm is shown to improve uniformly with the increase of the number of smoothing steps, without assuming full elliptic regularity. As a consequence, the -cycle convergence result of Braess and Hackbusch is generalized to problems without full elliptic regularity.
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Let Ω be a bounded domain with smooth boundary in . For the more general weight b, some nonlinearities f and singularities g, by two kinds of nonlinear transformations, a new perturbation method, which was introduced by García Melián in [J. García Melián, Boundary behavior of large solutions to elliptic equations with singular weights, Nonlinear Anal. 67 (2007) 818–826], and comparison principles, we show that the boundary behavior of solutions to a boundary blow-up elliptic problem Δw=b(x)f(w),w>0,xΩ,w|∂Ω=∞ and a singular Dirichlet problem −Δu=b(x)g(u),u>0,xΩ,u|∂Ω=0 has the same form under the nonlinear transformations, which can be determined in terms of the inverses of the transformations. 相似文献
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Cristian A. Coclici Gheorghe Moroanu Wolfgang L. Wendland 《Mathematical Methods in the Applied Sciences》2000,23(5):401-440
We consider a one‐dimensional coupled problem for elliptic second‐order ODEs with natural transmission conditions. In one subinterval, the coefficient ϵ>0 of the second derivative tends to zero. Then the equation becomes there hyperbolic and the natural transmission conditions are not fulfilled anymore. The solution of the degenerate coupled problem with a flux transmission condition is corrected by an internal boundary layer term taking into account the viscosity ϵ. By using singular perturbation techniques, we show that the remainders in our first‐order asymptotic expansion converge to zero uniformly. Our analysis provides an a posteriori correction procedure for the numerical treatment of exterior viscous compressible flow problems with coupled Navier–Stokes/Euler models. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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The nonlinear elliptic equation is investigated. It is supposed that u fulfils a mixed boundary value condition and that Ω ? IRn (n ≥ 3) has a piecewise smooth boundary. Ws,2 — regularity (s < 3/2) of u and Lp — properties of the first and the second derivatives of u are proven. 相似文献
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We prove existence and uniqueness results for non-linear elliptic equations with lower order terms, L1 data, and mixed boundary conditions that include as particular cases the Dirichlet and the Neumann problems.
Mathematics Subject Classification (2000) 35J25, 35D05, 35J70, 35J60 相似文献
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闻国椿 《数学物理学报(B辑英文版)》2007,27(3):663-672
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. 相似文献
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Gleiciane S. Aragão Simone M. Bruschi 《Mathematical Methods in the Applied Sciences》2016,39(12):3450-3460
In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior, which is uniformly Lipschitz and nonlinear terms, are concentrated in a region, which neighbors the boundary of domain. We prove that this family of solutions converges to the solutions of a limit problem in H1an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the
same equation:
- eDp u = f(x,u)inW, - \varepsilon \Delta _p u = f(x,u)in\Omega , 相似文献
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Stephan Dahlke 《manuscripta mathematica》1998,95(1):59-77
This paper is concerned with some theoretical foundations for adaptive numerical methods for elliptic boundary value problems.
The approximation order that can be achieved by such an adaptive method is determined by certain Besov regularity of the weak
solution. We study Besov regularity for second order elliptic problems in bounded domains in ℝ
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. The investigations are based on intermediate Schauder estimates and on some potential theoretic framework. Moreover, we
use characterizations of Besov spaces by wavelet expansions.
This work has been supported by the Deutsche Forschungsgemeinschaft (Da 360/1-1) 相似文献
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Guang Zhang 《Numerical Methods for Partial Differential Equations》2006,22(6):1479-1488
In this article, the existence of nontrivial solutions for the discrete elliptic boundary value problems is considered by using the extremum principle. Such system admits at least 2n nontrivial solutions when the nonlinear term is superlinear or sublinear. An explanation example is also given. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
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