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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GC22-08633J" target="_blank" >GC22-08633J: Kvalitativní teorie MHD a příbuzných rovnic</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Nonlinear Analysis: Theory, Methods & Applications

ISSN

0362-546X

e-ISSN

1873-5215

Svazek periodika

239

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

30

Strana od-do

113422

Kód UT WoS článku

001107721800001

EID výsledku v databázi Scopus

2-s2.0-85175247950