Existence of Optimal Control for Dirichlet Boundary Optimization in a Phase Field Problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00368437" target="_blank" >RIV/68407700:21340/23:00368437 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10883-023-09642-4" target="_blank" >https://doi.org/10.1007/s10883-023-09642-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10883-023-09642-4" target="_blank" >10.1007/s10883-023-09642-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Existence of Optimal Control for Dirichlet Boundary Optimization in a Phase Field Problem

Popis výsledku v původním jazyce

Phase field modeling finds utility in various areas. In optimization theory in particular, the distributed control and Neumann boundary control of phase field models have been investigated thoroughly. Dirichlet boundary control in parabolic equations is commonly addressed using the very weak formulation or an approximation by Robin boundary conditions. In this paper, the Dirichlet boundary control for a phase field model with a non-singular potential is investigated using the Dirichlet lift technique. The corresponding weak formulation is analyzed. Energy estimates and problem-specific embedding results are provided, leading to the existence and uniqueness of the solution for the state equation. These results together show that the control to state mapping is well defined and bounded. Based on the preceding findings, the optimization problem is shown to have a solution.

Název v anglickém jazyce

Existence of Optimal Control for Dirichlet Boundary Optimization in a Phase Field Problem

Popis výsledku anglicky

Phase field modeling finds utility in various areas. In optimization theory in particular, the distributed control and Neumann boundary control of phase field models have been investigated thoroughly. Dirichlet boundary control in parabolic equations is commonly addressed using the very weak formulation or an approximation by Robin boundary conditions. In this paper, the Dirichlet boundary control for a phase field model with a non-singular potential is investigated using the Dirichlet lift technique. The corresponding weak formulation is analyzed. Energy estimates and problem-specific embedding results are provided, leading to the existence and uniqueness of the solution for the state equation. These results together show that the control to state mapping is well defined and bounded. Based on the preceding findings, the optimization problem is shown to have a solution.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Dynamical and Control Systems

ISSN

1079-2724

e-ISSN

1573-8698

Svazek periodika

29

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

1425-1447

Kód UT WoS článku

000931641600001

EID výsledku v databázi Scopus

2-s2.0-85147989080