Abstract:
We apply the ,,User's Guide" on Dynamic programming
described recently by the first author to obtain the complete and
theoretically justified solution of a differential game considered
first by Breakwell and Bernhard. The optimal feedback
strategies and the corresponding value function are constructed
using a certain refinement of Cauchy's Method of characteristics
for stratified Hamilton-Jacobi equations while the optimality is
proved using a suitable ,,verification theorem" for
locally-Lipschitz value function. In fact, the partial and rather ,,artisanal"
solution in Breakwell and Bernhard of this problem, is not
only obtained by a general procedure but also ,,justified" in a
rigorous theoretical setting of suitable concepts and results.
Key Words: Differential game, Dynamic Programming,
feedback strategy, value function, verification theorem.
2000 Mathematics Subject Classification: Primary: 49N70,
Secondary 49N35, 91A23.
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