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 cylindrical domain under some necessary and sufficient conditions on the data. This elliptic problem is solved in Lp(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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