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Generalized linear models for population dynamics in two juxtaposed habitats

  • * Corresponding author: Alexandre Thorel

    * Corresponding author: Alexandre Thorel

The last author is supported by CIFRE contract 2014/1307 with Qualiom Eco company

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  • In this work we introduce a generalized linear model regulating the spread of population displayed in a $ d $-dimensional spatial region $ \Omega $ of $ \mathbb{R}^{d} $ constituted by two juxtaposed habitats having a common interface $ \Gamma $. This model is described by an operator $ \mathcal{L} $ of fourth order combining the Laplace and Biharmonic operators under some natural boundary and transmission conditions. We then invert explicitly this operator in $ L^{p} $-spaces using the $ H^{\infty } $-calculus and the Dore-Venni sums theory. This main result will lead us in a later work to study the nature of the semigroup generated by $ \mathcal{L} $ which is important for the study of the complete nonlinear generalized diffusion equation associated to it.

    Mathematics Subject Classification: 35B65, 35C15, 35J40, 35R20, 47A60, 47D06, 92D25.


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