Existence of Optimal Control for Dirichlet Boundary Optimization in a Phase Field Problem
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Existence of Optimal Control for Dirichlet Boundary Optimization in a Phase Field Problem
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Dynamical and Control Systems
ISSN
1079-2724
e-ISSN
1573-8698
Volume of the periodical
29
Issue of the periodical within the volume
10
Country of publishing house
CH - SWITZERLAND
Number of pages
23
Pages from-to
1425-1447
UT code for WoS article
000931641600001
EID of the result in the Scopus database
2-s2.0-85147989080