Controllability of second-order evolution systems in Banach spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F26867184%3A_____%2F25%3AN0000014" target="_blank" >RIV/26867184:_____/25:N0000014 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.aimspress.com/article/doi/10.3934/era.2025264" target="_blank" >https://www.aimspress.com/article/doi/10.3934/era.2025264</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3934/era.2025264" target="_blank" >10.3934/era.2025264</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Controllability of second-order evolution systems in Banach spaces

Popis výsledku v původním jazyce

This paper examines the controllability of the second-order evolution problems in Banach spaces in the presence of a nonlinear term depending on both the solution and its first derivative, and of a time-dependent linear term. The first goal of the paper is to introduce a definition of controllability for such problems that considers not only the solution but also its derivative at the final point using the same control function. Subsequently, the paper addresses the second goal: Finding conditions that guarantee the solvability of the controllability problem. The main statements of the paper are proved by the combination of Schauder fixed point theorem, approximate solvability, and weak topology. Using the method of approximate solvability allows us to avoid any compactness restrictions, and the results are therefore proved under non restrictive conditions imposed on the fundamental operator as well as on the right-hand side.

Název v anglickém jazyce

Controllability of second-order evolution systems in Banach spaces

Popis výsledku anglicky

This paper examines the controllability of the second-order evolution problems in Banach spaces in the presence of a nonlinear term depending on both the solution and its first derivative, and of a time-dependent linear term. The first goal of the paper is to introduce a definition of controllability for such problems that considers not only the solution but also its derivative at the final point using the same control function. Subsequently, the paper addresses the second goal: Finding conditions that guarantee the solvability of the controllability problem. The main statements of the paper are proved by the combination of Schauder fixed point theorem, approximate solvability, and weak topology. Using the method of approximate solvability allows us to avoid any compactness restrictions, and the results are therefore proved under non restrictive conditions imposed on the fundamental operator as well as on the right-hand side.

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

Electronic Research Archive

ISSN

2688-1594

e-ISSN

—

Svazek periodika

33

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

5937-5964

Kód UT WoS článku

001598720700003

EID výsledku v databázi Scopus

2-s2.0-105019377321