Title

Generalized functions in the qualitative study of heterogeneous populations

Document Type

Article

Publication Date

1-1-2019

Abstract

Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.

This document is currently not available here.

Share

COinS