Insensitizing control problems for the stabilized Kuramoto-Sivashinsky system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00599953" target="_blank" >RIV/67985840:_____/24:00599953 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1051/cocv/2024059" target="_blank" >https://doi.org/10.1051/cocv/2024059</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/cocv/2024059" target="_blank" >10.1051/cocv/2024059</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Insensitizing control problems for the stabilized Kuramoto-Sivashinsky system

Popis výsledku v původním jazyce

In this work, we address the existence of insensitizing controls for a nonlinear coupled system of fourth- and second-order parabolic equations known as the stabilized Kuramoto-Sivashinsky model. The main idea is to look for controls such that some functional of the states (the so-called sentinel) is locally insensitive to the perturbations of the initial data. Since the underlying model is coupled, we shall consider a sentinel in which we may observe one or two components of the system in a localized observation set. By some classical arguments, the insensitizing problem can be reduced to a null-controllability one for a cascade system where the number of equations is doubled. Upon linearization, the null-controllability for this new system is studied by means of Carleman estimates but unlike other insensitizing problems for scalar models, the election of the Carleman tools and the overall control strategy depends on the initial choice of the sentinel due to the (lack of) couplings arising in the extended system. Finally, the local null-controllability of the extended (nonlinear) system (and thus the insensitizing property) is obtained by applying the inverse mapping theorem.

Název v anglickém jazyce

Insensitizing control problems for the stabilized Kuramoto-Sivashinsky system

Popis výsledku anglicky

In this work, we address the existence of insensitizing controls for a nonlinear coupled system of fourth- and second-order parabolic equations known as the stabilized Kuramoto-Sivashinsky model. The main idea is to look for controls such that some functional of the states (the so-called sentinel) is locally insensitive to the perturbations of the initial data. Since the underlying model is coupled, we shall consider a sentinel in which we may observe one or two components of the system in a localized observation set. By some classical arguments, the insensitizing problem can be reduced to a null-controllability one for a cascade system where the number of equations is doubled. Upon linearization, the null-controllability for this new system is studied by means of Carleman estimates but unlike other insensitizing problems for scalar models, the election of the Carleman tools and the overall control strategy depends on the initial choice of the sentinel due to the (lack of) couplings arising in the extended system. Finally, the local null-controllability of the extended (nonlinear) system (and thus the insensitizing property) is obtained by applying the inverse mapping theorem.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

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

ESAIM-Control Optimisation and Calculus of Variations

ISSN

1292-8119

e-ISSN

1262-3377

Svazek periodika

30

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

45

Strana od-do

73

Kód UT WoS článku

001330548900007

EID výsledku v databázi Scopus

2-s2.0-85207101294