Well-Posed Nonlinear Problems

Autor:	Mircea Sofonea
EAN:	9783031414169
eBook Format:	PDF
Sprache:	Englisch
Produktart:	eBook
Veröffentlichungsdatum:	27.10.2023
Untertitel:	A Study of Mathematical Models of Contact
Kategorie:	Technik / Wissen
Schlagworte:	Well-posed problem;Well-posed nonlinear problems;Well-posedness;Nonlinear problems;Fixed-point problems;Inequality problems;Optimal control problems;Tykhonov triple;Contact problems;Contact mechanics;Convergence results;Variational inequalities;Hemiv

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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.

?Mircea Sofonea obtained the PhD degree at the University of Bucarest (Romania), and the habilitation at the Université Blaise Pascal of Clermont-Ferrand (France). Currently, he is a Distinguished Profesor at the University of Perpignan Via Domitia (France) and an Honorary Member of the Institute of Mathematics of the Romanian Academy of Sciences.

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.