Generalized functions in the qualitative study of heterogeneous populations

Natali Hritonenko, Yuri Yatsenko, Askar Boranbayev

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)146-162
Number of pages17
JournalMathematical Population Studies
Issue number3
Publication statusPublished - Jan 1 2019


  • age-distributed investment
  • age-structured population models
  • capital vintage
  • generalized functions
  • Optimal control
  • technological change

ASJC Scopus subject areas

  • Demography
  • Geography, Planning and Development
  • General Agricultural and Biological Sciences


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