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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

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

Mathematical Control and Related Fields

ISSN

2156-8472

e-ISSN

2156-8499

Svazek periodika

14

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

42

Strana od-do

1086-1127

Kód UT WoS článku

001081933700001

EID výsledku v databázi Scopus

2-s2.0-85197442566