[vc_empty_space][vc_empty_space]
Minimum of m-accretive operators and boundary value problems of hamilton-jacobi-bellman equation
Djafar M.K.a,b, Soeharyadi Y.a, Gunawan H.a
a Institut Teknologi Bandung, Indonesia
b Universitas Halu Oleo, Kendari, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2017 Pushpa Publishing House, Allahabad, India.In this article, boundary problems of the Hamilton-Jacobi-Bellman equation on the first quadrant of the Euclidean space ℝN are discussed. Well-posedness of the problem is discussed based on the well-posedness of the related family of the Hamilton-Jacobi equations. From nonlinear semigroup point of view, this amounts to establishing m-accretivity of the generator of the Hamilton-Jacobi-Bellman equation, as the minimum of a family of m-accretive generators of the related Hamilton-Jacobi equations. By the Crandall-Liggett theorem, well-posedness follows. Using symmetries, restrictions and invariances of the semigroups, the boundary value problem on the first quadrant of ℝN, namely Neumann BC is shown to be governed by strongly continuous, quasi contractive semigroups, and therefore wellposedness is established.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Boundary value problem,Hamilton-Jacobi-Bellman,M-accretive operator[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.17654/MS102051019[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]