摘要:

The paper is concerned with the application of Kantorovich (quasi-) majorants to the study of the convergence of Newton-Kantorovich approximations of solutions of nonlinear operator equations in Banach spaces. The derivative of the nonlinear operator is supposed to satisfy only a rather weak continuity condition. By means of an auxiliary scalar equation, we obtain convergence results for the Newton- Kantorovich approximations, as well as various new error estimates. The abstract results are illustrated by applications to nonlinear integral equations of Uryson type in the spaces C and.

ISSN:0163-0563    

DOI:10.1080/01630569708816744

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

In this paper one studies the existence of strong and variational-weak solutions for the multivalued stochastic differential equationThe uniqueness is proved for strong solutions and remains open for variational-weak solutions

ISSN:0163-0563    

DOI:10.1080/01630569708816745

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569708816746

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

Improving a recent result by the authors, a vector-valued version of Peano's Kernel Theorem is proposed, which gives an integral estimate for a class of linear operators, with X general normed space, vanishing on all abstract polynomials of degree < n. Continuity and derivatives are intended in the weak sense. When lthe space is complete, the usual integral representation is retrieved. We show that all usual remainder estimates for polynomial, piecewise polynomial, and spline polynomial interpolation, numerical differentiation and numerical quadrature, can be readily transferred in the vector-valued setting.

ISSN:0163-0563    

DOI:10.1080/01630569708816747

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

In this paper pseudoorbits of discrete dynamical systems are considered such that the one-step errors of the orbits tend to zero with increasing indices. First it is shown that close to hyperbolic sets such orbits are shadowed by true trajectories of the system with shadowing errors also tending to zero. Then the rates of convergence are studied via considering pseudoorbits such that the error sequences belong to certain (weighted) lp-spaces and showing that the corresponding shadowing errors are there, too. Under certain conditions on the weights we establish weighted shadowing near nonhyperbolic sets.

ISSN:0163-0563    

DOI:10.1080/01630569708816748

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

In this paper some properties of the embedding of nonlinear elliptic boundary value problems with discontinuities into families of smooth problems are investigated. The regularizations which are studied with respect to the related rate of convergence of the solutions of the smooth auxiliary problems to the the solution of the original discontinuous elliptic boundary value problem. In contrast to embedding methods for regular problems, naturally here an ill-conditioning occurs due to the approximation of boundary value problems with discontinuities. This yields a specific asymptotic convergence behaviour of Newton's method when applied to the regularized problems. The region of contraction of Newton's method is investigated and parameter selection rules are proposed such that truncated Newton iterations on each parameter level will generate an overall convergence of the resulting path-following technique. In addition some principles for the construction of monotone embedding methods for discontinuous elliptic boundary value problems are considered.

ISSN:0163-0563    

DOI:10.1080/01630569708816749

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

This paper studies the identifiability problem of stiffness and damping parameters and initial value problems in Euler-Bernoulli beam equations with Kelvin-Voigt damping. Using abstract evolution equation approach, we establish conditions for the identifiability of these parameters in beam equations. Analogous identifiability conditions for beam equations without damping are also established.

ISSN:0163-0563    

DOI:10.1080/01630569708816750

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

Let Ω denote the simplicial complexin Rd. For a nonnegative integerpwithlet Ω(p)denote the p- skeleton of Ω. Let d = 2 or 3 and suppose that f is a monotone function on Ω(1). We give construction schemes which extend f as a monotone function on Ω, while maintaining smoothness. Our results are related to those of Dahmen, DeVore and Micchelli for the case d = 2 and p = 1.

ISSN:0163-0563    

DOI:10.1080/01630569708816751

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

Earlier results for distributed and boundary controls of the viscous Burgers' equation were established by Burns et al. and Byrnes et al. In their results there are technical restrictions on the sizes of the initial data. In this paper we relax these restrictions, as well as treat the Burgers' equation with other nonlinear boundary conditions.

ISSN:0163-0563    

DOI:10.1080/01630569708816752

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

We describe how positive definite and conditionally negative definite functions on spheres can be used to carry out generalized interpolation on spheres.

ISSN:0163-0563    

DOI:10.1080/01630569708816753

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor