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Convergence of Global Solutions to the Cauchy Problem for the Replicator Equation in Spatial Economics

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  • Minoru Tabata
  • Nobuoki Eshima

Abstract

We study the initial‐value problem for the replicator equation of the N‐region Core‐Periphery model in spatial economics. The main result shows that if workers are sufficiently agglomerated in a region at the initial time, then the initial‐value problem has a unique global solution that converges to the equilibrium solution expressed by full agglomeration in that region.

Suggested Citation

  • Minoru Tabata & Nobuoki Eshima, 2016. "Convergence of Global Solutions to the Cauchy Problem for the Replicator Equation in Spatial Economics," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:4021516
    DOI: 10.1155/2016/4021516
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    References listed on IDEAS

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    Cited by:

    1. Kensuke Ohtake, 2025. "Pattern formation by advection-diffusion in new economic geography," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 48(2), pages 2157-2192, December.

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