The Cauchy problem for the nonlinear integro-partial differential equation in quantitative sociodynamics.
type: Item
instance of: scholarly article
title: The Cauchy problem for the nonlinear integro-partial differential equation in quantitative sociodynamics.
zbMATH Open document ID: 1033.45008
DOI: 10.1016/S0096-3003(01)00210-7
author: Minoru Tabata
author: Nobuoki Eshima
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The authors derive asymptotic estimates for solutions to the Cauchy problem for the generic (``master'') partial integro-differential equation \[ \partial v(t, x)/\partial t= -w(t, x)v(t,x)+ \int_{v\in D} W(t; x| y) v(t,y)\,dy, \] where \(D\subset\mathbb{R}^2\) is bounded and Lebesgue measurable; the kernel \(W(t;x| y)\) describes the transition rate, at time \(t\geq 0\), from the point \(y\in D\) to \(x\in D\). While such functional equations have their origin in statistical physics, the present paper is motivated by similar ones arising in quantitative sociodynamics, for example in the mathematical modelling of interregional migration due to regional economic disparity.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 91D10
zbMATH DE Number: 1861228
zbMATH Keywords: nonlinear partial integro-differential equation
zbMATH Keywords: asymptotics
zbMATH Keywords: quantitative sociodynamics
Wikidata QID: Q115339765
reviewed by: H. Brunner
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00210-7
OpenAlex ID: W2163220334
description: scientific article; zbMATH DE number 1861228