TY - CHAP
T1 - HamiltoN–Jacobi–Bellman equations on multi-domains
AU - Rao, Zhiping
AU - Zidani, Hasnaa
N1 - Publisher Copyright:
© Springer Basel 2013.
PY - 2013/1/1
Y1 - 2013/1/1
N2 - A system of Hamilton–Jacobi (HJ) equations on a partition of Rd is considered, and a uniqueness and existence result of viscosity solution is analyzed. While the notion of viscosity solution is by now well known, the question of uniqueness of solution, when the Hamiltonian is discontinuous, remains an important issue. A uniqueness result has been derived for a class of problems, where the behavior of the solution, in the region of discontinuity of the Hamiltonian, is assumed to be irrelevant and can be ignored (see (Camilli, Siconolfi in Adv. Differ. Equ. 8(6):733–768, 2003)). Here, we provide a new uniqueness result for a more general class of Hamilton–Jacobi equations.
AB - A system of Hamilton–Jacobi (HJ) equations on a partition of Rd is considered, and a uniqueness and existence result of viscosity solution is analyzed. While the notion of viscosity solution is by now well known, the question of uniqueness of solution, when the Hamiltonian is discontinuous, remains an important issue. A uniqueness result has been derived for a class of problems, where the behavior of the solution, in the region of discontinuity of the Hamiltonian, is assumed to be irrelevant and can be ignored (see (Camilli, Siconolfi in Adv. Differ. Equ. 8(6):733–768, 2003)). Here, we provide a new uniqueness result for a more general class of Hamilton–Jacobi equations.
KW - Discontinuous Hamiltonian
KW - Hamilton–Jacobi equations
KW - Optimal control
KW - Viscosity solution
UR - https://www.scopus.com/pages/publications/85093908093
U2 - 10.1007/978-3-0348-0631-2_6
DO - 10.1007/978-3-0348-0631-2_6
M3 - Chapter
AN - SCOPUS:85093908093
T3 - International Series of Numerical Mathematics
SP - 93
EP - 116
BT - International Series of Numerical Mathematics
PB - Springer Science and Business Media Deutschland GmbH
ER -