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Title
Well-posed nonlinear problems : a study of mathematical models of contact / Mircea Sofonea.
ISBN
9783031414169 (electronic bk.)
3031414160 (electronic bk.)
9783031414152
3031414152
Published
Cham : Birkhäuser, 2023.
Language
English
Description
1 online resource (407 pages) : illustrations (black and white, and color).
Item Number
10.1007/978-3-031-41416-9 doi
Call Number
QA427 .S64 2023
Dewey Decimal Classification
515/.355
Summary
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.
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Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Advances in mechanics and mathematics ; v. 50.
Part I An Abstract Well-posedness Concept
Nonlinear Problems and Their Solvability
Tykhonov Triples and Associate Well-posedness Concept
Part II Relevant Examples of Well-posed Problems
Fixed Point Problems
Variational Inequalities
Variational-hemivariational Inequalities
Inclusions and Sweeping Processes
Optimal Control and Optimization
Part III Well-posed Contact Problems
Preliminaries of Contact Mechanics
Well-posed Static Contact Problems. Well-posed Quasistatic Contact Problems.
