Insensitizing control problem for the Hirota–Satsuma system of KdV–KdV type

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00578002" target="_blank" >RIV/67985840:_____/24:00578002 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.na.2023.113422" target="_blank" >https://doi.org/10.1016/j.na.2023.113422</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2023.113422" target="_blank" >10.1016/j.na.2023.113422</a>

Result language
angličtina
Original language name
Insensitizing control problem for the Hirota–Satsuma system of KdV–KdV type
Original language description
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.
Czech name
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Czech description
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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
10101 - Pure mathematics

Project
<a href="/en/project/GC22-08633J" target="_blank" >GC22-08633J: Qualitative Theory of the MHD and Related Equations</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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