Viability Solutions to Hamilton–Jacobi Equations

Jean-Pierre Aubin (), Alexandre M. Bayen () and Patrick Saint-Pierre ()
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Jean-Pierre Aubin: VIMADES
Alexandre M. Bayen: University of California at Berkeley, Electrical Engineering and Computer Sciences Civil and Environmental Engineering
Patrick Saint-Pierre: Université Paris Dauphine LEDA-SDFi

Chapter Chapter 13 in Viability Theory, 2011, pp 523-561 from Springer

Abstract: Abstract This chapter presents the viability approach to a class of Hamilton-Jacobi equations. We assume not only that the solution depends on time, but on “structured” or “causal” variables. They include age-structured Hamilton-Jacobi-McKendrick equations, useful in population dynamics as well as in transport management (the age variable being replaced by the travel time), as well as Hamilton-Jacobi-Cournot equation, where the “structured” or “causal” variable is the initial state of the underlying control system. Chapters 14, p. 565 and 15, p. 605 apply the results of this chapter to transportation management, finance and economics.

Keywords: Viscosity Solution; Lower Semicontinuous; Optimal Evolution; Jacobi Equation; Viability Solution (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-16684-6_13

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DOI: 10.1007/978-3-642-16684-6_13

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