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Viability Solutions to Conservation Laws

In: Viability Theory

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jean-Pierre Aubin & Alexandre M. Bayen & Patrick Saint-Pierre, 2011. "Viability Solutions to Conservation Laws," Springer Books, in: Viability Theory, chapter 0, pages 631-680, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-16684-6_16
    DOI: 10.1007/978-3-642-16684-6_16
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