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On the regularity of a generalized diffusion problem arising in population dynamics set in a cylindrical domain

Abstract : In this paper, we consider a generalized diffusion problem arising in population dynamics. To this end, we study a fourth order operational equation of elliptic type, with various boundary conditions. We show existence, uniqueness and regularity of a classical solution on a cylindrica ldomain under some necessary and sufficient conditions on the data. This elliptic problem is solved in L^p(a,b;X), p∈(1,+∞), where (a,b)⊂R and X is a UMD Banach space. Our techniques use essentially the functional calculus and the semigroup theory.
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https://hal-normandie-univ.archives-ouvertes.fr/hal-02047101
Contributor : David Manceau <>
Submitted on : Saturday, February 23, 2019 - 6:15:30 PM
Last modification on : Monday, July 1, 2019 - 4:08:14 PM

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Rabah Labbas, Stéphane Maingot, David Manceau, Alexandre Thorel. On the regularity of a generalized diffusion problem arising in population dynamics set in a cylindrical domain. Journal of Mathematical Analysis and Applications, Elsevier, 2017, 450 (1), pp.351-376. ⟨10.1016/j.jmaa.2017.01.026⟩. ⟨hal-02047101⟩

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