Geometry of Optimal Paths around Focal Singular Surfaces in Differential Games
- Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Vernadsky Ave., 119526 Moscow (Russian Federation)
- University of Nice-Sophia Antipolis/CNRS I3S, ESSI, 930 Route des Colles, BP 145, 06903 Sophia Antipolis Cedex (France)
We investigate a special type of singularity in non-smooth solutions of first-order partial differential equations, with emphasis on Isaacs' equation. This type, called focal manifold, is characterized by the incoming trajectory fields on the two sides and a discontinuous gradient. We provide a complete set of constructive equations under various hypotheses on the singularity, culminating with the case where no a priori hypothesis on its geometry is known, and where the extremal trajectory fields need not be collinear. We show two examples of differential games exhibiting non-collinear fields of extremal trajectories on the focal manifold, one with a transversal approach and one with a tangential approach.
- OSTI ID:
- 21067440
- Journal Information:
- Applied Mathematics and Optimization, Vol. 52, Issue 1; Other Information: DOI: 10.1007/s00245-004-0816-8; Copyright (c) 2005 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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