1 edition of **A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling** found in the catalog.

- 352 Want to read
- 15 Currently reading

Published
**2002**
by Birkhäuser Basel, Imprint: Birkhäuser in Basel
.

Written in English

- Mathematics,
- Partial Differential equations

This monograph is devoted to the study of an evolutionary variational inequality approach to a degenerate moving free boundary problem. The inequality approach of obstacle type results from the application of an integral transformation. It takes an intermediate position between elliptic and parabolic inequalities and comprises an elliptic differential operator, a memory term and time-dependent convex constraint sets. The study of such inequality problems is motivated by applications to injection and compression moulding, to electro-chemical machining and other quasi-stationary Stefan type problems. The mathematical analysis of the problem covers existence, uniqueness, regularity and time evolution of the solution. This is carried out in the framework of the variational inequality theory. The numerical solution in two and three space dimensions is discussed using both finite element and finite volume approximations. Finally, a description of injection and compression moulding is presented in terms of different mathematical models, a generalized Hele-Shaw flow, a distance concept and Navier-Stokes flow. This volume is primarily addressed to applied mathematicians working in the field of nonlinear partial differential equations and their applications, especially those concerned with numerical aspects. However, the book will also be useful for scientists from the application areas, in particular, applied scientists from engineering and physics.

**Edition Notes**

Statement | by Jörg Steinbach |

Series | International Series of Numerical Mathematics -- 136, International series of numerical mathematics -- 136. |

Classifications | |
---|---|

LC Classifications | QA370-380 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (x, 294p.) |

Number of Pages | 294 |

ID Numbers | |

Open Library | OL27094089M |

ISBN 10 | 3034875991, 3034875975 |

ISBN 10 | 9783034875998, 9783034875974 |

OCLC/WorldCa | 851767492 |

The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary by: 8. Nonlinear Partial Differential Equations with Applications by Tomas Roubicek, , available at Book Depository with free delivery worldwide.

Variational Inequalities and Free Boundary Problems Xinfu Chen J Abstract This mini-course introduces some basic theory on free boundary prob-lems and its associated variational inequality problems. As an example, an American put problem will be thoroughly investigated. An outline of the course is as follows: Chapter 1 Variational. Variational inequality theory is an important tool in studying a wide class of obstacle, unilateral, and equilibrium problems arising in several branches of pure and applied sciences in a uniﬁed and general framework [3,4,12,17,18,24]. This ﬁeld is dynamic and is experiencing an explosive growth in both theory and applications.

A NEW PROJECTION METHOD FOR VARIATIONAL INEQUALITY PROBLEMS M. V. SOLODOV yAND B. F. SVAITER SIAM J. CONTROL OPTIM. °c Society for Industrial and Applied Mathematics Vol. 37, No. 3, pp. { Abstract. We propose a new projection algorithm for . variational inequality formulation is that the location of the contact area (free boundary) becomes an integral part of the solution and no special de-vices are needed to locate it. Variational inequality approach enables us not only to study the problem of the existence of solution of obstacle problems.

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Since the early s, the mathematical theory of variational inequalities has been under rapid development, based on complex analysis and strongly influenced by 'real-life' application.

Many, but of course not all, moving free (Le., a priori un known) boundary problems originating fromBrand: Birkhäuser Basel. Buy A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling (International Series of Numerical Mathematics) Cited by: 7.

A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling. Authors (view affiliations) Jörg Steinbach; Book. but of course not all, moving free (Le., a priori un known) boundary problems originating from engineering and economic applica tions can directly, or after a transformation, be formulated.

11R Variational Inequality Approach to Free Boundary Problems with Applications in Mould Filling. ISNM, Vol -J Steinbach (Gartnerstr 8, Augsburg, Author: J Steinbach, L Mishnaevsky. Get this from a library.

A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling. [Jörg Steinbach] -- This monograph is devoted to the study of an evolutionary variational inequality approach to a degenerate moving free boundary problem.

The inequality approach of obstacle type results from the. variational and free boundary problems Download variational and free boundary problems or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get variational and free boundary problems book now. This site is like a library, Use search box in the widget to get ebook that you want. Get this from a library. A variational inequality approach to free boundary problems with applications in mould filling.

[Jörg Steinbach, (Professor of mathematics)]. variational principles and free boundary problems Download variational principles and free boundary problems or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get variational principles and free boundary problems book now. This site is like a library, Use search box in the widget to get ebook.

Abstract. In the previous chapter we saw that a variational inequality approach to the general moving free boundary problem () leads to obstacle problems of the form () which should be investigated in the sequel in a slightly more general : Jörg Steinbach.

In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the.

Variational inequality theory was introduced by Hart-man and Stampacchia () as a tool for the study of partial di erential equations with applications principally drawn from mechanics. Such variational inequalities were in nite-dimensional rather than nite-dimensional as we will be studying here.

The breakthrough in nite-dimensional theory File Size: KB. Key Words: Variational inequalities, monotonicity properties, applications. 1 Variational Inequalities with Continuous Map-pings We rst consider the main results in theory of variational inequality problems with continuous single-valued mappings and their relationships with other general problems of Nonlinear Analysis.

Problem FormulationFile Size: KB. Free and moving boundary problems occur in such varied subjects as hydrology, heat flow, metallurgy, molecular diffusion, flame propagation, steel and glass production, and oil drilling and mathematical finance.

This book presents a comprehensive account of the mathematical formulation of suchproblems and many new methods of solution.

Variational inequalities (equilibrium or evolution problems typically with convex constraints) are carefully explained in An Introduction to Variational Inequalities and Their Applications.

They are shown to be extremely useful across a wide variety of subjects, ranging from linear programming to free boundary problems in partial differential Cited by: Energy Methods for Free Boundary Problems: Applications to Nonlinear PDEs and Fluid Mechanics can serve as a reference on the subject of energy methods when they are treated as part of mathematics post-graduate Variational Inequality Approach to Free Boundary Problems with Applications in Mould Filling.

ISNM, Vol Appl. Mech. Rev Cited by: Full Description: "The problem of developing metal matrix (MCM) and metal-polymer (MPCM) composite materials is one of the most important in present day materials technology, for its solution is pivotal to the development of a number of leading technologies.

The development of new fibrous and lamellar composite materials with improved physico-chemical, electrical, thermal and other properties. An Introduction to Variational Inequalities and Their Applications David Kinderlehrer, Guido Stampacchia Limited preview - David Kinderlehrer, Guido Stampacchia Limited preview - Numerical Solution of the Incompressible Navier-Stokes Equations A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling.

1 The incompressible Navier-Stokes equations.- Introduction.- Incompressible Navier-Stokes equations.- Organization of the book.- Some references.- 2. A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals.

We are looking for maximal values of the solution with respect to. However, for some problems governed by the variational inequality, there are very few approaches.

As far as we know, it is hard to find any applicable methods except for those of Nakao and Ryoo. The theory of variational inequalities has become a rich source of inspiration in both mathematical and engineering by: 3.

Asymptotic behavior for the free boundary of parabolic variational inequalities and applications to sequential analysis Friedman, Avner, Illinois Journal of Mathematics, ; The free boundary for a fourth order variational inequality Caffarelli, Luis A., Friedman, Avner, and Torelli, Alessandro, Illinois Journal of Mathematics, C.W.

Cryer, Successive overrelaxation methods for solving linear complementarity problems arising from free boundary problems, in: E. Magenes, ed. Free Boundary Problems l (Ist. Naz. Alta Mat. F. Severi, Rome, ) ontributed significantly to the analysis of the variational inequality formulation of free-boundary problems (see [5] for Author: M A Boudourides, J A Hitiroglou.Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms and Applications.

Article (PDF Available) in Mathematical Programming 48(1)