
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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Article accepté pour publication ou publiéDate
2023Journal name
Mathematics in EngineeringVolume
5Number
1Publisher
AIMS Press
Pages
1-23
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Show full item recordAbstract (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 InequalityRelated items
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