The behavior of solutions to the Cauchy problem for the master equation

DOI10.1016/S0096-3003(99)00050-8zbMath1023.45007OpenAlexW2075983462MaRDI QIDQ1569219

Minoru Tabata, Nobuoki Eshima

Publication date: 25 June 2000

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(99)00050-8

zbMATH Keywords

Cauchy problemnonlinearmaster equationsintegro-partial differential equationsquantitative sociodynamics

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Other nonlinear integral equations (45G10) Models of societies, social and urban evolution (91D10)

Related Items (10)

The behavior of stochastic agent-based models when the number of agents and the time variable tend to infinity ⋮ The Kramers-Moyal expansion of the master equation that describes human migration in a bounded domain ⋮ A geometrical similarity between migration of human population and diffusion of biological particles ⋮ A self-referential agent-based model that consists of a large number of agents moving stochastically in a discrete bounded domain. ⋮ A mathematical modeling approach to the formation of urban and rural areas: convergence of global solutions of the mixed problem for the master equation in sociodynamics ⋮ A mathematical-model approach to human population explosions caused by migration ⋮ Mathematical representations of the dynamics of social system. I: General description ⋮ An infinite continuous model which derives from a finite discrete model describing the time evolution of the density of firms. ⋮ Blowing-up solutions to the Cauchy problem for the master equation ⋮ The Cauchy problem for the nonlinear integro-partial differential equation in quantitative sociodynamics.

Cites Work

• Synergetic economics. Time and change in nonlinear economics
• Chaos and socio-spatial dynamics
• The nonlinear integro-partial differential equation describing the logistic growth of human population with migration
• The Cauchy problem for the system of equations describing migration motivated by regional economic disparity
• Concepts and models of a quantitative sociology. The dynamics of interacting populations
• Quantitative sociodynamics. Stochastic methods and models of social interaction processes. Transl. from the German by Richard Calek and Dirk Helbing

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