M-ACCRETIVE OPERATOR AND APPLICATION FOR BOUNDARY VALUE PROBLEM OF HAMILTON-JACOBI-BELLMAN EQUATION

• Main Author: KABIL DJAFAR , MUHAMMAD
• Format: Dissertations
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/29277
• Institution: Institut Teknologi Bandung

<p align="justify">The focus of this research is semigroup theoretic approach applied to a boundary <br /> <br /> 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 <br /> <br /> 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 <br /> <br /> 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 <br /> <br /> satisfies generally Neumann boundary condition on the boundary, thereby solving generalize Neumann boundary condition for Hamilton-Jacobi-Bellman equation.<p align="justify">