Local null-controllability of a system coupling Kuramoto-Sivashinsky-KdV and elliptic equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00570784" target="_blank" >RIV/67985840:_____/23:00570784 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2023.127213" target="_blank" >https://doi.org/10.1016/j.jmaa.2023.127213</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2023.127213" target="_blank" >10.1016/j.jmaa.2023.127213</a>

Result language
angličtina
Original language name
Local null-controllability of a system coupling Kuramoto-Sivashinsky-KdV and elliptic equations
Original language description
This paper deals with the null-controllability of a system of mixed parabolic-elliptic pdes at any given time T>0. More precisely, we consider the Kuramoto-Sivashinsky–Korteweg-de Vries equation coupled with a second order elliptic equation posed in the interval (0,1). We first show that the linearized system is globally null-controllable by means of a localized interior control acting on either the KS-KdV or the elliptic equation. Using the Carleman approach, we provide the existence of a control with the explicit cost CeC/T with some constant C>0 independent in T. Then, applying the source term method developed in [39], followed by the Banach fixed point theorem, we conclude the small-time local null-controllability result of the nonlinear system.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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