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Insensitizing control problem for the Hirota–Satsuma system of KdV–KdV type
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SYSNO ASEP 0578002 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Insensitizing control problem for the Hirota–Satsuma system of KdV–KdV type Tvůrce(i) Bhandari, Kuntal (MU-W) SAI, ORCID Číslo článku 113422 Zdroj.dok. Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 239, February (2024)Poč.str. 30 s. Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova Korteweg-de Vries system ; insensitizing control ; Carleman estimate ; inverse mapping theorem 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 001107721800001 EID SCOPUS 85175247950 DOI https://doi.org/10.1016/j.na.2023.113422 Anotace This paper is concerned with the existence of insensitizing controls for a nonlinear coupled system of two Korteweg-de Vries (KdV) equations, typically known as the Hirota-Satsuma system. The idea is to look for controls such that some functional of the states (the so-called sentinel) is insensitive to the small perturbations of initial data. Since the system is coupled, we consider a sentinel in which we observe both components of the system in a localized observation set. By some classical argument, the insensitizing problem is then reduced to a null-control problem for an extended system where the number of equations is doubled. We study the null-controllability for the linearized model associated to that extended system by means of a suitable Carleman estimate which is proved in this paper. Finally, the local null-controllability of the extended (nonlinear) system is obtained by applying the inverse mapping theorem, and this implies the required insensitizing property for the concerned model. 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/10.1016/j.na.2023.113422
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