On a new concept of controllability of second-order semilinear differential equations in Banach spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F26867184%3A_____%2F25%3AN0000011" target="_blank" >RIV/26867184:_____/25:N0000011 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.aimsciences.org//article/doi/10.3934/mcrf.2025002" target="_blank" >https://www.aimsciences.org//article/doi/10.3934/mcrf.2025002</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3934/mcrf.2025002" target="_blank" >10.3934/mcrf.2025002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On a new concept of controllability of second-order semilinear differential equations in Banach spaces

Popis výsledku v původním jazyce

In this paper, the controllability of second-order problems in Banach spaces is investigated when the nonlinear term also depends on the first derivative. The main aim of the paper is to introduce the definition of controllability for second-order problems in Banach spaces that considers both the solution and its derivative at the final point using a unique control and to obtain sufficient conditions for such controllability. Our main results are derived by combining the Schauder fixed point theorem with the approximation solvability method and weak topology. This approach allows us to obtain results under easily verifiable and non-restrictive conditions imposed on the cosine family generated by the linear operator and on the right-hand side since any requirements for compactness are avoided. The paper concludes by applying the obtained results to a system governed by the one-dimensional Klein-Gordon equation.

Název v anglickém jazyce

On a new concept of controllability of second-order semilinear differential equations in Banach spaces

Popis výsledku anglicky

In this paper, the controllability of second-order problems in Banach spaces is investigated when the nonlinear term also depends on the first derivative. The main aim of the paper is to introduce the definition of controllability for second-order problems in Banach spaces that considers both the solution and its derivative at the final point using a unique control and to obtain sufficient conditions for such controllability. Our main results are derived by combining the Schauder fixed point theorem with the approximation solvability method and weak topology. This approach allows us to obtain results under easily verifiable and non-restrictive conditions imposed on the cosine family generated by the linear operator and on the right-hand side since any requirements for compactness are avoided. The paper concludes by applying the obtained results to a system governed by the one-dimensional Klein-Gordon equation.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

N - Vyzkumna aktivita podporovana z neverejnych zdroju

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

AIMS - American Institute of Mathematical Sciences

ISSN

2156-8472

e-ISSN

—

Svazek periodika

15

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

1150-1173

Kód UT WoS článku

001400213800001

EID výsledku v databázi Scopus

2-s2.0-105003427274