Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions
- Authors: Adly, Samir , Hantoute, Abderrahim , Théra, Michel
- Date: 2012
- Type: Text , Journal article
- Relation: Nonlinear Analysis: Theory, Methods & Applications Vol. 75, no. 3 (February, 2012), p. 985-1008
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- Description: The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative. We also propose a unifying review of many other criteria given in the literature. Our approach is based on advanced tools of variational analysis and generalized differentiation.
A new regularity criterion of weak solutions to the 3D micropolar fluid flows in terms of the pressure
- Authors: Gala, Sadek , Ragusa, Maria , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Bolletino dell Unione Matematica Italiana Vol. 14, no. 2 (2021), p. 331-337
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: In this study, we establish a new regularity criterion of weak solutions to the three-dimensional micropolar fluid flows by imposing a critical growth condition on the pressure field. © 2020, Unione Matematica Italiana.
Enlargements of the moreau–rockafellar subdifferential
- Authors: Abbasi, Malek , Kruger, Alexander , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 29, no. 3 (2021), p. 701-719
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: This paper proposes three enlargements of the conventional Moreau–Rockafellar subdifferential: the sup-, sup
Orthogonality in locally convex spaces : two nonlinear generalizations of Neumann's lemma
- Authors: Barbagallo, Annamaria , Ernst, Octavian-Emil , Théra, Michel
- Date: 2020
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 484, no. 1 (Apr 2020), p. 18
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- Description: In this note we prove a symmetric version of the Neumann lemma as well as a symmetric version of the Soderlind-Campanato lemma. We establish in this way two partial generalizations of the well-known Casazza-Christenses lemma. This work is related to the Birkhoff-James orthogonality and to the concept of near operators introduced by S. Campanato. (C) 2019 Published by Elsevier Inc.
Strongly regular points of mappings
- Authors: Abbasi, Malek , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Fixed Point Theory and Algorithms for Sciences and Engineering Vol. 2021, no. 1 (Journal article 2021), p.
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- Description: In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient of the error bound. © 2021, The Author(s).
Directional metric pseudo subregularity of set-valued mappings: a general model
- Authors: Van Ngai, Huynh , Tron, Nguyen , Van Vu, Nguyen , Théra, Michel
- Date: 2020
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 28, no. 1 (2020), p. 61-87
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- Description: This paper investigates a new general pseudo subregularity model which unifies some important nonlinear (sub)regularity models studied recently in the literature. Some slope and abstract coderivative characterizations are established. © 2019, Springer Nature B.V.
On the regularity of weak solutions of the boussinesq equations in besov spaces
- Authors: Barbagallo, Annamaria , Gala, Sadek , Ragusa, Maria , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Vietnam Journal of Mathematics Vol. 49, no. 3 (2021), p. 637-649
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: The main issue addressed in this paper concerns an extension of a result by Z. Zhang who proved, in the context of the homogeneous Besov space Ḃ