M-ACCRETIVE OPERATOR AND APPLICATION FOR BOUNDARY VALUE PROBLEM OF HAMILTON-JACOBI-BELLMAN EQUATION - KABIL DJAFAR , MUHAMMAD
The focus of this research is semigroup theoretic approach applied to a boundary value problem of Hamilton-Jacobi-Bellman equation. The first part of this research is to construct minimum of collection of m-accretive operators in the Banach space of bounded and uniformly continuous functions on RN. For a finite collection of m-accretive operators, the minimum can be shown to be m-accretive. For countable collection of m-accretive operators, however, we turn to the notice of graphconvergent. Suitably defined, the minimum is also m-accretive. Since m-accretive operator generate strongly continuous semigroup, by Crandall-Liggett Theorem, this minimum operator is related to a partial differential equation, which happen to be the Hamilton-Jacobi-Bellman equation. By restricting the semigroup action on E-invariant subspace, the solution to the partial differential equation naturally satisfies generally Neumann boundary condition on the boundary, thereby solving generalize Neumann boundary condition for Hamilton-Jacobi-Bellman equation.