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On a Boltzmann mean field model for knowledge growth
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Burger, M., Lorz, A. and Wolfram, Marie-Therese (2016) On a Boltzmann mean field model for knowledge growth. SIAM Journal on Applied Mathematics, 76 (5). pp. 1799-1818. doi:10.1137/15M1018599 ISSN 0036-1399.
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Official URL: http://doi.org/10.1137/15M1018599
Abstract
In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll [15]. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analytic features of each equation separately and show local in time existence and uniqueness for the fully coupled system. Furthermore we focus on the construction and existence of special solutions, which relate to exponential growth in time - so called balanced growth path solutions. Finally we illustrate the behavior of solutions for the full system and the balanced growth path equations with numerical simulations.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | SIAM Journal on Applied Mathematics | ||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||
ISSN: | 0036-1399 | ||||||
Official Date: | 8 September 2016 | ||||||
Dates: |
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Volume: | 76 | ||||||
Number: | 5 | ||||||
Page Range: | pp. 1799-1818 | ||||||
DOI: | 10.1137/15M1018599 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 19 July 2016 | ||||||
Date of first compliant Open Access: | 3 May 2017 | ||||||
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