Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a Neumann control

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a Neumann control

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a Neumann control

Popis výsledku anglicky

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.

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

Evolution Equations and Control Theory

ISSN

2163-2480

e-ISSN

2163-2480

Svazek periodika

13

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

587-615

Kód UT WoS článku

001126654100001

EID výsledku v databázi Scopus

2-s2.0-85184734570