Abstract
In this chapter we study the well-posedness of inclusions. We start with a stationary inclusion for which we prove the well-posedness with various Tykhonov triples, together with several convergence results, including a convergence criterion. We extend a part of these results to a history-dependent inclusion. The proofs are based on the results obtained in Chap. 3, in the study of fixed point problems. Finally, we consider a history-dependent variational inequality with time-dependent constraints and perform its analysis by using arguments of duality introduced in Sect. 2.2. Given a Tykhonov triple, everywhere in this chapter we use the notation and definitions introduced in Sect. 2.1.2.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Sofonea, Tykhonov triples and convergence analysis for an inclusion problem, Bulletin Mathématique la Société Mathématique de Roumanie65 (2022), 73–96.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Sofonea, M. (2023). Inclusions. In: Well-Posed Nonlinear Problems. Advances in Mechanics and Mathematics, vol 50. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-41416-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-031-41416-9_6
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-41415-2
Online ISBN: 978-3-031-41416-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)