Polterovich, Victor and Henkin, Gennadi (1998): A Differencedifferential Analogue of the Burgers Equation and Some Models of Economic Development.

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Abstract
The paper is devoted to investigation of a number of differencedifferential equations, among them the following one plays the central role: dFn/dt<=φ(Fn)(Fn1  Fn) (*) where, for every t, {Fn(t), n = 0, 1, 2, ...} is a probability distribution function, and φ is a positive function on [0, 1]. The equation (*) arose as a description of industrial economic development taking into account processes of creation and propagation of new technologies. The paper contains a survey of the earlier received results including a multydimensional generalization and an application to the economic growth theory.
If φ is decreasing then solutions of the Cauchy problem for (*) approach to a family of wavetrains. We show that diffusionwise asymptotic behavior takes place if φ is increasing. For the nonmonotonic case a general hypothesis about asymptotic behavior is formulated and an analogue of a Weinberger's (1990) theorem is proved. It is argued that the equation can be considered as an analogue of Burgers equation.
Item Type:  MPRA Paper 

Original Title:  A Differencedifferential Analogue of the Burgers Equation and Some Models of Economic Development 
Language:  English 
Keywords:  differencedifferential equations; Burgers equations; nonlinear diffusion; longtime asymptotic of Cauchy problem; evolution of industries; economic growth; innovation and imitation processes 
Subjects:  O  Economic Development, Technological Change, and Growth > O4  Economic Growth and Aggregate Productivity > O41  One, Two, and Multisector Growth Models O  Economic Development, Technological Change, and Growth > O3  Technological Change; Research and Development; Intellectual Property Rights > O33  Technological Change: Choices and Consequences; Diffusion Processes 
Item ID:  21031 
Depositing User:  Victor Polterovich 
Date Deposited:  04. Mar 2010 03:22 
Last Modified:  20. Feb 2013 23:13 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/21031 