Overview
- Presents an original method that unifies the mathematical theories of well-posed problems and contact mechanics
- Offers a well-posedness theory in which every convergence result can be interpreted as a well-posedness result
- Provides a unitary treatment of contact models, featuring new variational formulations and convergence results
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 50)
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Table of contents (10 chapters)
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Front Matter
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An Introduction to Well-Posedness of Nonlinear Problems
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Front Matter
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Relevant Examples of Well-Posed Problems
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Front Matter
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Well-Posed Contact Problems
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Front Matter
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Back Matter
Keywords
About this book
This monograph presents an original method to unify the mathematical theories of well-posed problems and contact mechanics. The author uses a new concept called the Tykhonov triple to develop a well-posedness theory in which every convergence result can be interpreted as a well-posedness result. This will be useful for studying a wide class of nonlinear problems, including fixed-point problems, inequality problems, and optimal control problems. Another unique feature of the manuscript is the unitary treatment of mathematical models of contact, for which new variational formulations and convergence results are presented. Well-Posed Nonlinear Problems will be a valuable resource for PhD students and researchers studying contact problems. It will also be accessible to interested researchers in related fields, such as physics, mechanics, engineering, and operations research.
Authors and Affiliations
About the author
His areas of interest and expertise include : multivalued operators, variational and hemivariational inequalities, solid mechanics, contact mechanics and numerical methods for partial differential equations.
Most of his reseach is dedicated to the Mathematical Theory of Contact Mechanics, of which he is one of the main contributors. His ideas and results were published in eight books, four monographs, and more than three hundred research articles.
Bibliographic Information
Book Title: Well-Posed Nonlinear Problems
Book Subtitle: A Study of Mathematical Models of Contact
Authors: Mircea Sofonea
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-031-41416-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-41415-2Published: 28 October 2023
Softcover ISBN: 978-3-031-41418-3Due: 28 November 2023
eBook ISBN: 978-3-031-41416-9Published: 27 October 2023
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 1
Number of Pages: XVIII, 405
Number of Illustrations: 14 b/w illustrations, 1 illustrations in colour
Topics: Optimization, Mathematical Modeling and Industrial Mathematics, Operator Theory, Solid Mechanics, Analysis