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Burgers type equations, Gelfand’s problem and Schumpeterian dynamics

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Abstract

Burgers’ equations have been introduced to study different models of fluids (Bateman, 1915, Burgers, 1939, Hopf, 1950, Cole, 1951, Lighthill andWhitham, 1955, etc.). The difference-differential analogues of these equations have been proposed for Schumpeterian models of economic development (Iwai, 1984, Polterovich and Henkin, 1988, Belenky, 1990, Henkin and Polterovich, 1999, Tashlitskaya and Shananin, 2000, etc.).

This paper gives a short survey of the results and conjectures on Burgers type equations, motivated both by fluid mechanics and by Schumpeterian dynamics. Proofs of some new results are given. This paper is an extension and an improvement of (Henkin, 2007, 2011).

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Authors and Affiliations

  1. Université Pierre et Marie Curie, case 247, 75252, Paris, France

    G. M. Henkin

  2. CEMI, Academy of Science, 117418, Moscow, Russia

    G. M. Henkin

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Correspondence to G. M. Henkin.

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To Professor Richard Palais on the occasion of his 80th birthday

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Henkin, G.M. Burgers type equations, Gelfand’s problem and Schumpeterian dynamics. J. Fixed Point Theory Appl. 11, 199–223 (2012). https://doi.org/10.1007/s11784-012-0089-9

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