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Équation de diffusion généralisée pour un modèle de croissance et de dispersion d'une population incluant des comportements individuels à la frontière des divers habitats

Abstract : The aim of this work is the study of a transmission problem in population dynamics between two juxtaposed habitats. In each habitat, we consider a partial differential equation, modeling the generalized dispersion, made up of a linear combination of Laplacian and Bilaplacian operators. We begin by studying and solving the same equation with various boundary conditions in a single habitat. This study is carried out using an operational formulation of the problem: we rewrite this PDE as a differential equation, set in a Banach space built on the spaces Lp with 1 < p < +∞, where the coefficients are unbounded linear operators. Thanks to functional calculus, analytic semigroup theory and interpolation theory, we obtain optimal results of existence, uniqueness and maximum regularity of the classical solution if and only if the data are in some interpolation spaces.
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Alexandre Thorel. Équation de diffusion généralisée pour un modèle de croissance et de dispersion d'une population incluant des comportements individuels à la frontière des divers habitats. Equations aux dérivées partielles [math.AP]. Normandie Université, 2018. Français. ⟨NNT : 2018NORMLH07⟩. ⟨tel-01818039⟩

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