Evolution inclusions and variation inequalities for Earth data Processing. I. Operator inclusions and variation inequalities for earth data processing.
type: Item
instance of: scholarly article
title: Evolution inclusions and variation inequalities for Earth data Processing. I. Operator inclusions and variation inequalities for earth data processing.
zbMATH Open document ID: 1213.47001
DOI: 10.1007/978-3-642-13837-9
author: Pavlo O. Kasyanov
author: Michael Z. Zgurovsky
author: V. S. Mel'nik
published in: Advances in Mechanics and Mathematics
publication date: 2010-08-11T00:00:00Z
review text: In the investigation of various mathematical models describing transient states of systems, there often appear situations when the model includes ordinary or partial differential equations with discontinuous or multivalued functions. There arises the problem of developing a theoretical apparatus for the constructive and systems analysis of such mathematical objects as differential operator inclusions and hemivariational inequalities. This problem requires the study of new classes of multivalued maps of monotone type, the verification of new methods for the search for approximate solutions, and many other topics. The book under review is devoted to the analysis of these problems. The monograph consists of two volumes. The first volume contains the systematic investigation of various classes of monotone type operators and the application of the obtained results to the study of boundary value problems with non-smooth and non-coercive interaction function and stationary variational inequalities. The contents of the first volume are the following. Chapter 1. Preliminary results. 1.1. The main results from multivalued mappings theory. 1.2. Classes of multivalued maps. 1.3. Subdifferentials in infinite-dimensional spaces. 1.4. Minimax inequalities in finite-dimensional spaces. Chapter 2. Operator inclusions and variational inequalities in infinite-dimensional spaces. 2.1. Strong solutions for parametrized operator inclusions. 2.2. Parametrized operator inequalities. 2.3. Variational inequalities in Banach and Frechet spaces. 2.4. The penalty method for multivariational inequalities. 2.5. Nonlinear operator equations of the Hammerstein type. Systems of operators equations. 2.6. Nonlinear non-coercive operator equations and their normalization. 2.7. Some examples connected with membranes theory. [For Part II, see Zbl 1213.47002.]
reviewed by: B. D. Gel'man
Mathematics Subject Classification ID: 47-02
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47J22
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 86A10
zbMATH DE Number: 5768423
zbMATH Keywords: multivalued map
zbMATH Keywords: monotone map
zbMATH Keywords: subdifferential
zbMATH Keywords: minimax inequality
zbMATH Keywords: evolution inclusion
zbMATH Keywords: operator inclusion
zbMATH Keywords: operator equation
zbMATH Keywords: variational inequality
zbMATH Keywords: operator inequality
zbMATH Keywords: penalty method
zbMATH Keywords: non-coercive operator equation
zbMATH Keywords: membranes theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-13837-9
OpenAlex ID: W2483731017
description: scientific article; zbMATH DE number 5768423