Local exact controllability to the steady states of a parabolic system with coupled nonlinear boundary conditions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00577243" target="_blank" >RIV/67985840:_____/24:00577243 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3934/mcrf.2023035" target="_blank" >https://doi.org/10.3934/mcrf.2023035</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/mcrf.2023035" target="_blank" >10.3934/mcrf.2023035</a>

Result language
angličtina
Original language name
Local exact controllability to the steady states of a parabolic system with coupled nonlinear boundary conditions
Original language description
In this article, we study the boundary local exact controllability to any steady state of a one˦dimensional parabolic system with coupled nonlinear boundary conditions by means of only one control. The significant point is that the state components are interacting only at the boundary points with the assistance of some nonlinear terms. We consider two cases: either the control function is acting through a mixed nonlinear boundary condition on the first component or through a Neumann condition on the second component. The results are slightly different in the two cases. To study this problem, we first consider the associated linearized systems around the given steady state. The method of moments let us to prove its controllability and to obtain a suitable estimate of the control cost of the form MeM(T+ T1). To this end, we need to develop a precise spectral analysis of a non self˦adjoint operator. Thanks to those preliminary results, we can use the source term method developed in [29], followed by the Banach fixed point argument, to obtain the small˦time boundary local exact controllability to the steady state for the original 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
<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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