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Convergence analysis for elliptic quasivariational inequalities

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Abstract

We deal with a class of elliptic quasivariational inequalities with constraints in a reflexive Banach space. We use arguments of monotonicity, convexity and compactness in order to prove a convergence criterion for such inequalities. This criterion allows us to consider a new well-posedness concept in the study of the corresponding inequalities, which extends the classical Tykhonov and Levitin–Polyak well-posedness concepts used in the literature. Then, we introduce a new penalty method, for which we provide a convergence result. Finally, we consider a variational inequality which describes the equilibrium of a spring–rods system, under the action of external forces. We apply our abstract results in the study of this inequality and provide the corresponding mechanical interpretations. We also present numerical simulations which validate our convergence results.

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Acknowledgements

This project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No 823731 CONMECH.

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  1. Laboratoire de Mathématiques et Physique, University of Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860, Perpignan, France

    Mikael Barboteu & Mircea Sofonea

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  1. Mikael Barboteu
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  2. Mircea Sofonea
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Correspondence to Mircea Sofonea.

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Barboteu, M., Sofonea, M. Convergence analysis for elliptic quasivariational inequalities. Z. Angew. Math. Phys. 74, 130 (2023). https://doi.org/10.1007/s00033-023-02022-9

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  • DOI: https://doi.org/10.1007/s00033-023-02022-9

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