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

R Labbas (1) , S Maingot (1) , D Manceau (1) , A Thorel (1)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

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 cylindrical domain 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.

Mots clés: Population dynamics; Abstract differential equations; UMD spaces; Bounded imaginary powers; Interpolation spaces; Maximal regularity

Domaines: Equations aux dérivées partielles [math.AP]

R Labbas, S Maingot, D Manceau, A Thorel. On the regularity of a generalized diffusion problem arising in population dynamics set in a cylindrical domain. 2016. ⟨hal-01342758⟩