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Non-smooth variational problems and applications Full article

Journal Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
ISSN: 1364-503X
Output data Year: 2022, Volume: 380, Number: 2236, Article number : 20210364, Pages count : 3 DOI: 10.1098/rsta.2021.0364
Tags continuum mechanics; non-smooth variational methods
Authors Kovtunenko Victor A. 1 , Itou Hiromichi 2 , Khludnev Alexander M. 3 , Rudoy Evgeny M. 3,4
Affiliations
1 Institute for Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstr. 36, 8010 Graz, Austria
2 2 Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
3 Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
4 Novosibirsk State University, Department of Mathematics and Mechanics, 630090 Novosibirsk, Russia

Abstract: Mathematical methods based on the variational approach are successfully used in a broad range of applications, especially those fields that are oriented on partial differential equations. Our problem area addresses a wide class of nonlinear variational problems described by all kinds of static and evolution equations, inverse and ill-posed problems, non-smooth and non-convex optimization, and optimal control including shape and topology optimization. Within these directions, we focus but are not limited to singular and unilaterally constrained problems arising in mechanics and physics, which are governed by complex systems of generalized variational equations and inequalities. Whereas classical mathematical tools are not applicable here, we aim at a non-standard well-posedness analysis, numerical methods, asymptotic and approximation techniques including homogenization, which are successful within the primal as well as the dual variational formalism. In a broad scope, the theme issue objectives are directed toward advances that are attained in the mathematical theory of non-smooth variational problems, its physical consistency, numerical simulation and application to engineering sciences.This article is part of the theme issue ‘Non-smooth variational problems and applications’.
Cite: Kovtunenko V.A. , Itou H. , Khludnev A.M. , Rudoy E.M.
Non-smooth variational problems and applications
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2022. V.380. N2236. 20210364 :1-3. DOI: 10.1098/rsta.2021.0364 WOS Scopus РИНЦ OpenAlex
Dates:
Submitted: Jul 28, 2022
Accepted: Jul 29, 2022
Published print: Sep 26, 2022
Identifiers:
Web of science: WOS:000861201200005
Scopus: 2-s2.0-85138524003
Elibrary: 56665272
OpenAlex: W4297143864
Citing:
DB Citing
Scopus 4
Web of science 3
OpenAlex 5
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