ISSN:0163-0563    

DOI:10.1080/01630569808816811

出版商:Marcel Dakker Inc.    

年代:1998

数据来源: Taylor

摘要:

We apply the boundary integral equation method and a primal mixed finite element approach to study the weak solvability and Galerkin approximations of linear interior transmission problems arising in potential theory and elastostatics. The existence and uniqueness of solution of the resulting weak formulations and of the associated discrete schemes are derived by using the classical theory for variational problems with constraints. Suitable finite element subspaces of Lagrange type satisfying the compatibility conditions are utilized for defining the Galerkin scheme. The error analysis and corresponding rates of convergence are also provided.

ISSN:0163-0563    

DOI:10.1080/01630569808816812

出版商:Marcel Dekker,Inc.    

年代:1998

数据来源: Taylor

摘要:

Letbe nonexpansive mappings on a Hilbert space H, and letbe a function which has a uniformly strongly positive and uniformly bounded second (Fréchet) derivative over the convex hull of Ti(H) for some i. We first prove that Θ has a unique minimum over the intersection of the fixed point sets of all the Ti’s at some point u*. Then a cyclic hybrid steepest descent algorithm is proposed and we prove that it converges to u*. This generalizes some recent results of Wittmann (1992), Combettes (1995), Bauschke (1996), and Yamada, Ogura, Yamashita, and Sakaniwa (1997).

ISSN:0163-0563    

DOI:10.1080/01630569808816813

出版商:Marcel Dakker Inc.,    

年代:1998

数据来源: Taylor

摘要:

The one-dimensional wave equation that is coupled to oscillators at the boundaries is approximated using Legendre polynomials. The convergence of the corresponding semigroups is proven by means of Trotter-Kato theory. By expansion of the characteristic determinants it is shown that the transfer functions of the approximate systems arc those of the exact system with the exponential functions replaced by Padé fractions.

ISSN:0163-0563    

DOI:10.1080/01630569808816814

出版商:Marcel Dakker Inc.,    

年代:1998

数据来源: Taylor

摘要:

Let M be a bounded metric space and supposesatisfies for some fixedfor all x,y€M. It is shown that under this assumption, for certain spaces M there will always exist z€M such that. If M is a convex subset of a Banach space, then weak compactness and normal structure suffice. If M is a hyperconvex metric space (in particular, if M is an intersection of closed balls in l∞) then there always exists z €M such that. Mappings of the type considered arise naturally. For example if K is a convex subset of a Banach space and if h,p€(0,1], then mappingswhich are Hölder continuous in the senseobviously satisfy the weaker condition.

ISSN:0163-0563    

DOI:10.1080/01630569808816815

出版商:Marcel Dakker Inc.    

年代:1998

数据来源: Taylor

摘要:

In [6] [7], the coefficients of given equation are supposed to be Lipschitz continuity or to be a bit weaker than Lipschitz continuity for establishing existence and uniqueness of the solution. In this paper, we show that, under the assumption of so-called pathwise uniqueness to the equation, a weaker restriction to coefficients than these mentioned above will recapture the convergence of Carathéodory approximation of the equation in the strong sense.

ISSN:0163-0563    

DOI:10.1080/01630569808816816

出版商:Marcel Dakker Inc.,    

年代:1998

数据来源: Taylor

摘要:

This paper attempts to answer an open question on the uniform stabilizability of a commonly used finite difference method for the approximation of a control system modeled by 1-dimensional weakly damped wave equation. A detailed analysis of the spectral properties of the matrices used in the approximation and the asymptotic properties of the eigenvalues as a function of the dimension of the approximation space allow to conclude that finite dimensional control systems given by the approximation method considered here are not uniformly stabilizable. The results on the spectral properties of the matrices used in the finite difference approximation of the partial differential equations discussed in this paper also provide a method to calculate each individual eigenvalues of the matrix through a scalar iterative method. It is used in this paper to obtain accurate estimates on the stability and stabilizability margins of the finite dimensional control systems as well as to compute the eigenvalues numerically to verify our theoretical results.

ISSN:0163-0563    

DOI:10.1080/01630569808816817

出版商:Marcel Dakker Inc.,    

年代:1998

数据来源: Taylor

摘要:

Main result: For each closed convex subset C of a Banach space X and eachthere exists an equivalent norm on X for which x has a unique nearest point in C.

ISSN:0163-0563    

DOI:10.1080/01630569808816818

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper, we study necessary and sufficient optimality conditions for multiobjective optimization problems in general case and we derive the results of Corley [4] as a consequence.

ISSN:0163-0563    

DOI:10.1080/01630569808816819

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

The equilibrium problem concerning vector functions is formulated and some results on the existence of equilibrium points for this problem are proved and applied to vector optimizations , Nash equilibrium in noncooperative games, variational inequalities etc. concerning vector functions

ISSN:0163-0563    

DOI:10.1080/01630569808816820

出版商:Marcel Decker. Inc    

年代:1998

数据来源: Taylor