Functional Differential Equations Arising in Cell-growth

Abstract

Non-local differential equations are notoriously difficult to solve. Cell-growth models for population growth of a cohort structured by size, simultaneously growing and dividing, give rise to a class of non-local eigenvalue problems, whose principal” eigenvalue is the time-constant for growth/decay. These and other novel non-local problems are described and solved in special cases in this paper. Keywords: Non-local differential equations; non-local eigenvalue problems; delay equation; pantograph equation; zero-flux condition; cohort of cells; Green’s function