Viability Solutions to Conservation Laws

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 16 in Viability Theory, 2011, pp 631-680 from Springer

Abstract: Abstract Several chapters (Chaps. 13,p. 525, 14,p. 525, 17,p. 525,and Sects. 15,p. and 525) are devoted to first-order Hamilton-Jacobi-Bellman partial differential equations. This chapter presets a viability approach to another class of partial differential equations, conservation laws. We restrict our study to the Burgers equation (the canonical example of conservation laws) in Sect. 16.2,p. 525 for illustrating this approach.We also include in this chapter the short Sect. 16.3, p.569 to a generalization of the Invariant Manifold Theorem to control problems which plays an important of control theory. It is an addendum to Chap. 8 of the first edition of Viability Theory [18,A ubin] (1991) which is not repeated in this second edition.

Keywords: Dirichlet Boundary Condition; Burger Equation; Viability Solution; Viability Theory; Lagrangian Condition (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_16

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DOI: 10.1007/978-3-642-16684-6_16

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