Local Null-Controllability for Some Quasi-Linear Phase-Field Systems with Neumann Boundary Conditions by one Control Force

Shengzhu Shi, Dazhi Zhang and Wei Zhang

Discrete Dynamics in Nature and Society, 2022, vol. 2022, 1-16

Abstract: In this article, we study the local null-controllability for some quasi-linear phase-field systems with homogeneous Neumann boundary conditions and an arbitrary located internal controller in the frame of classical solutions. In order to minimize the number of control forces, we prove the Carleman inequality for the associated linear system. By constructing a sequence of optimal control problems and an iteration method based on the parabolic regularity, we find a qualified control in Hölder space for the linear system. Based on the theory of Kakutani’s fixed point theorem, we prove that the quasi-linear system is local null-controllable when the initial datum is small and smooth enough.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ddns/2022/7645304.pdf (application/pdf)
http://downloads.hindawi.com/journals/ddns/2022/7645304.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:7645304

DOI: 10.1155/2022/7645304

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().