Abstract
We introduce solutions of boundary-value problems for the stationary Hamilton-Jacobi and Bellman equations in functional spaces (semimodules) with a special algebraic structure adapted to these problems. In these spaces, we obtain representations of solutions in terms of “basic” ones and prove a theorem on approximation of these solutions in the case where nonsmooth Hamiltonians are approximated by smooth Hamiltonians. This approach is an alternative to the maximum principle.
Similar content being viewed by others
References
V. P. Maslov, “A new superposition principle for problems of optimization,” Usp. Mat. Nauk, 225, 39–48 (1989).
V. Kolokol’tsov and V. P. Maslov, “Idempotent analysis as a tool in the theory of control,” Funkts. Anal. Prilozh., 23, No. 1, 1–11 (1989); No. 4, 300–307 (1990).
V. P. Maslov and S. N. Samborski (editors), Idempotent Analysis, in: Advances in Soviet Mathematics, 13, American Mathematical Society (1992).
V. P. Maslov and S. N. Samborski, “Boundary value problems for stationary Hamilton-Jacobi and Bellman equations,” in: Lect. Notes Control Inf. Sci., Springer, 197, 456–465 (1993).
S. Samborski, “Lagrange problem from the point of view of idempotent analysis,” Proc. Newton Inst., Cambridge University Press, Cambridge (1996).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 433–447, March, 1997.
Rights and permissions
About this article
Cite this article
Maslov, V.P., Samborskii, S.N. Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations. Ukr Math J 49, 477–493 (1997). https://doi.org/10.1007/BF02487244
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487244