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Some comparison results and a partial bang-bang property for two-phases problems in balls

Mazari, Idriss (2023), Some comparison results and a partial bang-bang property for two-phases problems in balls, Mathematics in Engineering, 5, 1, p. 1-23. 10.3934/mine.2023010

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Type
Article accepté pour publication ou publié
Date
2023
Journal name
Mathematics in Engineering
Volume
5
Number
1
Publisher
AIMS Press
Pages
1-23
Publication identifier
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Author(s)
Mazari, Idriss
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this paper, we present two type of contributions to the study of two-phases problems. In such problems, the main focus is on optimising a diffusion function a under L ∞ and L 1 constraints, this function a appearing in a diffusive term of the form −∇ • (a∇) in the model, in order to maximise a certain criterion. We provide a parabolic Talenti inequality and a partial bang-bang property in radial geometries for a general class of elliptic optimisation problems: namely, if a radial solution exists, then it must saturate, at almost every point, the L ∞ constraints defining the admissible class. This is done using an oscillatory method.
Subjects / Keywords
Optimisation; Optimal Control of PDEs; Two-Phases Problems; Talenti Inequality