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A Class of Nonlinear Inclusions and Sweeping Processes in Solid Mechanics

We consider a new class of inclusions in Hilbert spaces for which we provide an existence and uniqueness result. The proof is based on arguments of monotonicity, convexity and fixed point. We use this result to establish the unique solvability of an associated class of Moreau’s sweeping processes. N...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2021-02, Vol.171 (1), Article 16
Main Authors: Nacry, Florent, Sofonea, Mircea
Format: Article
Language:English
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Summary:We consider a new class of inclusions in Hilbert spaces for which we provide an existence and uniqueness result. The proof is based on arguments of monotonicity, convexity and fixed point. We use this result to establish the unique solvability of an associated class of Moreau’s sweeping processes. Next, we give two applications in Solid Mechanics. The first one concerns the study of a time-dependent constitutive law with unilateral constraints and memory term. The second one is related to a frictional contact problem for viscoelastic materials. For both problems we describe the physical setting, list the assumptions on the data and provide existence and uniqueness results.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-020-00380-4