Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a Neumann control
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00583247" target="_blank" >RIV/67985840:_____/24:00583247 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3934/eect.2023059" target="_blank" >https://doi.org/10.3934/eect.2023059</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/eect.2023059" target="_blank" >10.3934/eect.2023059</a>
Alternative languages
Result language
angličtina
Original language name
Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a Neumann control
Original language description
This article is concerned with the local boundary null-controll-ability of a 1-D system of two-parabolic nonlinear equations (often referred as reaction-diffusion system) with coupled boundary conditions by means of a scalar control. The control force is exerted on one of the two state components through a Neumann condition at the left end of the boundary while the other component simply satisfies the homogeneous Neumann condition at that point. On the other hand, at the right end of the boundary, the states are coupled through the so-called δ′-type condition. Upon linearization around the stationary point (0, 0), we apply the well-known moments method to prove the global null-controllability of the associated linearized system with explicit control cost MeM/T as T → 0+. Then, we show the local null-controllability of the main system by employing the source term method developed in [29] followed by the Banach fixed point theorem.
Czech name
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Czech description
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Classification
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
Result continuities
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
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Evolution Equations and Control Theory
ISSN
2163-2480
e-ISSN
2163-2480
Volume of the periodical
13
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
587-615
UT code for WoS article
001126654100001
EID of the result in the Scopus database
2-s2.0-85184734570