[LAMPS] Convergence analysis of systems with fixed point structure

Résumé

This paper investigates the existence, uniqueness, and convergence of solutions for a general problem involving two sets, X and Y, and subsets P, Q in the Cartesian product X x Y. The authors demonstrate that finding a pair (u, η) in P x Q is equivalent to finding fixe points of specific operators, Λ and Θ. In the context of metric spaces, the study provides necessary and sufficient conditions for the convergence of sequences to the solution. These abstract result are applied to three complex nonlinear systems : an elliptic hemivariational inequality coupled with a minimization problem, a system of variational inequalities related to piezoelectric contact, and a differential variational inequality. For each, existence and uniqueness are established, with convergence criteria provided for the first two examples.

Mots clés : fixed point, convergence criterion, variational inequality, hemivariational inequality, minimization problem, differential variational inequality.

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Intervenant

Bruno Vassallo, LAMPS, UPVD