3 edition of Variational method and method of monotone operators in the theory of nonlinear equations found in the catalog.
Variational method and method of monotone operators in the theory of nonlinear equations
M. M. VaiМ†nberg
|Statement||[by] M. M. Vainberg. Translated from Russian by A. Libin. Translation edited by D. Louvish.|
|LC Classifications||QA372 .V3213|
|The Physical Object|
|Pagination||xi, 356 p.|
|Number of Pages||356|
|LC Control Number||73016383|
This is the first and only book to prove in a systematic and unifying way, stability, convergence and computing results for the different numerical methods for nonlinear elliptic problems. The proofs use linearization, compact perturbation of the coercive principal parts, or monotone operator techniques, and approximation theory. Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, and create an exciting interplay. Other books discuss nonlinearity by a very few important examples. This is the first and only book, proving in a systematic and unifying way, stability and convergence results and methods for solving nonlinear discrete equations via discrete Newton methods.
The notion of monotone operators was introduced by Zarantonello [Zarantonello, ], Minty [Minty, ] and Ka˘ curovskii [Ka˘ curovskii, ]. Monotonicity conditions in the context of variational methods for nonlinear operator equations were also used by Vainberg and Ka˘ curovskii [Vainberg et al., ]. A map A: D(A) H!H is monotone if. This variational approach to maximal monotone operators allows their theory to be analyzed with the full range of methods –computational or not – that are available for variational settings. Standard convex analysis (on phase space) can then be used to establish many old and new results concerned with the identification, superposition, and.
6. Concluding Remarks. In this work, we have developed the family of primal-dual active set methods to solve the discrete nonlinear systems, arising from the variational inequality problems with -monotone operators. We build the equivalent relation between the primal-dual active set method and Howard’s algorithm, then show the convergence theorem of Howard’s algorithm, and thus obtain the. variational methods () Filter by: Remove filter variational inequalities | split inexact Uzawa method | MONOTONE-OPERATORS Full Text Exp-function method for nonlinear wave equations. by He, Ji-Huan and Wu, Xu-Hong. Chaos, solitons and fractals, ISSN , , Vol Issue 3, pp. -
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Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations Hardcover – Import, January 1, by M M Vainberg (Author) See all formats and editions Hide other formats and editionsCited by: Get this from a library. Variational method and method of monotone operators in the theory of nonlinear equations.
[M M Vaĭnberg; Alexander Libin; David Louvish]. Variational method and method of monotone operators in the theory of nonlinear equations. New York, Wiley [, ©] (OCoLC) Document Type: Book: All Authors /. A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper.
A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping rule. Numerical experiments show that the proposed stopping rule is efficient. It is divided into two subvolumes, II/A and II/B, which form a unit.
The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of.
equations. This method was first proposed, for linear operators, by Morse and Feshbach , under the name of “adjoint operator method”. This method was extended to the general, nonlinear case by Finlayson .
The method of integrating operator consists in considering, instead of the operator. Fixed Point Theory and Related Topics Author: Wu, Hsien-Chung ISBN: Year: Pages: DOI: /books Language: English. Our approach uses variational methods based on the critical point theory, truncation and perturbation techniques, and Morse theory (critical groups).
Article information. Source N.S. Papageorgiou and V. Staicu, Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints, Mem. Amer. Math. Soc. Abstract. This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods.
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence.
Our results apply to approximations such as explicit finite difference schemes and Trotter–Kato type mixing formulas. About this book Introduction Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years.
This paper focuses on the problem of variational inequalities with monotone operators in real Hilbert space. The Tseng algorithm constructed by Thong replaced a high-precision step.
Thus, a new Tseng-like gradient method is constructed, and the convergence of the algorithm is proved, and the convergence performance is higher. This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis.
The presentation is self-contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. Jeong Sheok Ume's research works with 1, citations and 1, reads, including: C-class Functions and Common Fixed Point Theorems Satisfying φ-weakly Contractive Conditions.
M.M. Vainberg, "Variational method and method of monotone operators in the theory of nonlinear equations", Wiley () (Translated from Russian)  H. Gajewski, K. Gröger, K. Zacharias, "Nichtlineare Operatorengleichungen und Operatorendifferentialgleichungen", Akademie Verlag ().
Variational Methods for the Study of Nonlinear Operators. With a chapter on Newton's Method by Vainberg, M. M., Kantorovich, Akilov, G. and a great selection of related books, art and collectibles available now at This variational approach to maximal monotone operators allows their theory to be analyzed with the full range of methods --computational or not-- that are available for variational settings.
Variational Methods and Method of Monotone Operators in the Theory of Nonlinear Equations, John Wiley, New York (). This book is devoted to the study of nonlinear evolution and difference equations of first and second order governed by a maximal monotone operator.
This class of abstract evolution equations contains not only a class of ordinary differential equations, but also unify some important partial differential equations, such as the heat equation. The aim the paper is to study a large class of variational-hemivariational inequalities involving constraints in a Banach space.
First, we establish a. This book is concerned with basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. This is a monograph about the most significant results obtained in this area in last decades but is also.Using this framework we derive global convergence results and iteration-complexity bounds for a family of projective splitting methods for solving monotone inclusion problems, which generalize the projective splitting methods introduced and studied by Eckstein and Svaiter (SIAM J .M.M.
Vainberg, V.A. Trenogin, "Theory of branching of solutions of non-linear equations", Noordhoff () (Translated from Russian)  M.M. Vainberg, "Variational methods and methods of nonlinear operators in the theory of nonlinear equations", Wiley () (Translated from Russian) .