The nonlinear integro-partial differential equation describing the logistic growth of human population with migration

摘要

We derive a nonlinear integro-partial differential equation which describes the logistic growth of human population with migration. The equation is based upon the theory of logistic growth of population and upon the theory of migration in quantitative sociodynamics. We prove that the Cauchy problem for the equation has a unique global solution, and we obtain fundamental estimates for the solution.