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

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 is an element of (1, + infinity), where (a, b) subset of R and X is a UMD Banach space. Our techniques use essentially the functional calculus and the semigroup theory. (C) 2017 Elsevier Inc. All rights reserved.