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Local exact controllability to the steady states of a parabolic system with coupled nonlinear boundary conditions
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SYSNO ASEP 0577243 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Local exact controllability to the steady states of a parabolic system with coupled nonlinear boundary conditions Tvůrce(i) Bhandari, Kuntal (MU-W) SAI, ORCID
Boyer, F. (FR)Zdroj.dok. Mathematical Control and Related Fields - ISSN 2156-8472
Roč. 14, č. 3 (2024), s. 1086-1127Poč.str. 42 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova boundary controllability ; fixed˦point argument ; method of moments Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GC22-08633J GA ČR - Grantová agentura ČR Způsob publikování Omezený přístup Institucionální podpora MU-W - RVO:67985840 UT WOS 001081933700001 EID SCOPUS 85197442566 DOI https://doi.org/10.3934/mcrf.2023035 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2025 Elektronická adresa https://doi.org/10.3934/mcrf.2023035
Počet záznamů: 1