Number of the records: 1
Local exact controllability to the steady states of a parabolic system with coupled nonlinear boundary conditions
- 1.
SYSNO ASEP 0577243 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Local exact controllability to the steady states of a parabolic system with coupled nonlinear boundary conditions Author(s) Bhandari, Kuntal (MU-W) SAI, ORCID
Boyer, F. (FR)Source Title Mathematical Control and Related Fields - ISSN 2156-8472
Roč. 14, č. 3 (2024), s. 1086-1127Number of pages 42 s. Language eng - English Country US - United States Keywords boundary controllability ; fixed˦point argument ; method of moments Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GC22-08633J GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 001081933700001 EID SCOPUS 85197442566 DOI https://doi.org/10.3934/mcrf.2023035 Annotation In this article, we study the boundary local exact controllability to any steady state of a one˦dimensional parabolic system with coupled nonlinear boundary conditions by means of only one control. The significant point is that the state components are interacting only at the boundary points with the assistance of some nonlinear terms. We consider two cases: either the control function is acting through a mixed nonlinear boundary condition on the first component or through a Neumann condition on the second component. The results are slightly different in the two cases. To study this problem, we first consider the associated linearized systems around the given steady state. The method of moments let us to prove its controllability and to obtain a suitable estimate of the control cost of the form MeM(T+ T1). To this end, we need to develop a precise spectral analysis of a non self˦adjoint operator. Thanks to those preliminary results, we can use the source term method developed in [29], followed by the Banach fixed point argument, to obtain the small˦time boundary local exact controllability to the steady state for the original system. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2025 Electronic address https://doi.org/10.3934/mcrf.2023035
Number of the records: 1