On Duality Principles and Concerned Convex Dual Formulations Applied to a Non-Linear Plate Theory and Related Models

Fabio Botelho

doi:10.20944/preprints202409.0460.v2

Preprint Article Version 2 This version is not peer-reviewed

Version 1 : Received: 5 September 2024 / Approved: 5 September 2024 / Online: 5 September 2024 (12:43:44 CEST)
Version 2 : Received: 6 September 2024 / Approved: 9 September 2024 / Online: 9 September 2024 (12:01:56 CEST)

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual approximate variational formulation for a non-linear Kirchhoff-Love plate model. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual approximate formulation obtained may be applied to a large class of similar models in the calculus of variations. Finally, in the last section, we present a duality principle and respective convex dual formulation for a Ginzburg-Landau type equation.

duality principle; non-linear plate model; convex dual approximate formulation

Computer Science and Mathematics, Applied Mathematics

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On Duality Principles and Concerned Convex Dual Formulations Applied to a Non-Linear Plate Theory and Related Models

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