A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling

Jörg Steinbach

ISBN 10: 3034875991 / ISBN 13: 9783034875998

Published by Birkhäuser Basel Sep 2012, 2012

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -This monograph studies an evolutionary variational inequality approach to a degenerate moving free boundary problem. 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. 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. 308 pp. Englisch.

Seller Inventory # 9783034875998

Bibliographic Details

• Title: A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling
• Publisher: Birkhäuser Basel Sep 2012
• Publication Date: 2012
• Language: English
• ISBN 10: 3034875991
• ISBN 13: 9783034875998
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 244W x 170H x 17D millimeters 244 millimeters width by 170 millimeters height by 17 millimeters depth
• Weight: 535 grams

About this title

Synopsis

Since the early 1960s, 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 from engineering and economic applica­ tions can directly, or after a transformation, be formulated as variational inequal­ ities. In this work we investigate an evolutionary variational inequality with a memory term which is, as a fixed domain formulation, the result of the application of such a transformation to a degenerate moving free boundary problem. This study includes mathematical modelling, existence, uniqueness and regularity results, numerical analysis of finite element and finite volume approximations, as well as numerical simulation results for applications in polymer processing. Essential parts of these research notes were developed during my work at the Chair of Applied Mathematics (LAM) of the Technical University Munich. I would like to express my sincerest gratitude to K. -H. Hoffmann, the head of this chair and the present scientific director of the Center of Advanced European Studies and Research (caesar), for his encouragement and support. With this work I am fol­ lowing a general concept of Applied Mathematics to which he directed my interest and which, based on application problems, comprises mathematical modelling, mathematical and numerical analysis, computational aspects and visualization of simulation results.