Burgers type equations, Gelfand's problem and Schumpeterian dynamics

Guennadi Khenkine (1)

1 IMJ - Institut de Mathématiques de Jussieu

Burgers equations have been introduced to study different models of fluids Bateman, 1915, Burgers, 1939, Hopf, 1950, Cole, 1951, Lighthill, Whitham, 1955.... The difference-differential analogs of these equations have been proposed for Schumpeterian models of economic development Iwai, 1984, Polterovich, Henkin, 1988, Belenky, 1990, 1996, Henkin, Polterovich, 1999, Shananin, Tashlitskaya, 2000.... This paper is a survey of recent results and conjectures on Burgers type equations, motivated both by fluid mechanics and by Schumpeterian dynamics. Abriged proofs of new results are given. This paper is an extended version of the paper [Henkin, 2011] prepared for the talk at the conference "General Equilibrium Analysis" at Higher School of Economics, June, 2011.

Domaines: Equations aux dérivées partielles [math.AP]

Guennadi Khenkine. Burgers type equations, Gelfand's problem and Schumpeterian dynamics. 2012. ⟨hal-00692144⟩