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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Viability Solutions to Conservation Laws
verfasst von : Prof. Jean-Pierre Aubin, Prof. Dr.-Ing. Alexandre M. Bayen, Prof. Patrick Saint-Pierre
Erschienen in: Viability Theory
Verlag: Springer Berlin Heidelberg
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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.