Abstract
Our primary aims are to investigate a specific version of the classical macroeconomics model, known as the Keynes business cycle model together with spatial factors. This will then lead us to analyzing a system of differential equations that are of parabolic type. This system can be reduced to a scalar partial differential equation supplemented by the homogeneous Neumann boundary conditions.The sufficient conditions with spatially nonhomogeneous equilibrium states will be obtained for our boundary value problem. As a result, asymptotic formulas will be obtained for such solutions. The analysis of the problem is based on the methods of modern theory of dynamical systems with an infinite-dimensional space of initial conditions. The obtained results will show the assumption of the ‘‘distribution of the economy in space.’’ In addition, we will also show that the results substantially complement the description of economic dynamics in comparison with the ‘‘traditional’’ models that apply ordinary differential equations.
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Funding
This work was carried out within the framework of a development programme for the Regional Scientific and Educational Mathematical Center of the Yaroslavl State University with financial support from the Ministry of Science and Higher Education of the Russian Federation (Agreement on provision of subsidy from the federal budget no. 075-02-2022-886).
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Kulikov, A.N., Kulikov, D.A. & Radin, M.A. Analysis of Keynes’s Mathematical Model—Effect of Spatial Factors. Lobachevskii J Math 43, 1345–1357 (2022). https://doi.org/10.1134/S1995080222090165
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DOI: https://doi.org/10.1134/S1995080222090165