Homogenization for operators with arbitrary perturbations in coefficients

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021094" target="_blank" >RIV/62690094:18470/23:50021094 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jde.2023.05.048" target="_blank" >https://doi.org/10.1016/j.jde.2023.05.048</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2023.05.048" target="_blank" >10.1016/j.jde.2023.05.048</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Homogenization for operators with arbitrary perturbations in coefficients

Popis výsledku v původním jazyce

We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. We perturbed it by a first order differential operator arbitrarily depending on a small multi-dimensional parameter and we study the existence of a limiting (homogenized) operator in the sense of the norm resolvent convergence. The first part of our main results states that the norm resolvent convergence is equivalent to the convergence of the coefficients in the perturbing operator in certain space of multipliers. The second part of our results says that the convergence in the mentioned spaces of multipliers is equivalent to the convergence of certain local mean values over small pieces of the considered domains. These results are supported by series of examples. We also provide a series of ways of generating new non-periodically oscillating perturbations for which our results are applicable.&amp; COPY; 2023 Elsevier Inc. All reserved.

Název v anglickém jazyce

Homogenization for operators with arbitrary perturbations in coefficients

Popis výsledku anglicky

We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. We perturbed it by a first order differential operator arbitrarily depending on a small multi-dimensional parameter and we study the existence of a limiting (homogenized) operator in the sense of the norm resolvent convergence. The first part of our main results states that the norm resolvent convergence is equivalent to the convergence of the coefficients in the perturbing operator in certain space of multipliers. The second part of our results says that the convergence in the mentioned spaces of multipliers is equivalent to the convergence of certain local mean values over small pieces of the considered domains. These results are supported by series of examples. We also provide a series of ways of generating new non-periodically oscillating perturbations for which our results are applicable.&amp; COPY; 2023 Elsevier Inc. All reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-18739S" target="_blank" >GA22-18739S: Asymptotická a spektrální analýza operátorů v matematické fyzice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Journal of differential equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

369

Číslo periodika v rámci svazku

October

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

53

Strana od-do

41-93

Kód UT WoS článku

001024726500001

EID výsledku v databázi Scopus

2-s2.0-85161645642