Convergence estimates for abstract second-order singularly perturbed Cauchy problems with Lipschitzian nonlinearities

Perjan Andrei; Rusu Galina

Conţinutul numărului revistei

Articolul precedent

Articolul urmator

SM ISO690:2012

PERJAN, Andrei, RUSU, Galina. Convergence estimates for abstract second-order singularly perturbed Cauchy problems with Lipschitzian nonlinearities. In: Asymptotic Analysis, 2011, vol. 74, pp. 135-165. ISSN 0921-7134. DOI: https://doi.org/10.3233/ASY-2011-1043

EXPORT metadate:
Google Scholar
Crossref
CERIF

DataCite
Dublin Core

Asymptotic Analysis

Volumul 74 / 2011 / ISSN 0921-7134 /ISSNe 1875-8576

Convergence estimates for abstract second-order singularly perturbed Cauchy problems with Lipschitzian nonlinearities

DOI:https://doi.org/10.3233/ASY-2011-1043

Pag. 135-165

Perjan Andrei, Rusu Galina

Moldova State University

Disponibil în IBN: 5 martie 2024

Descarcă PDF

Rezumat

We study the behavior of solutions to the problem ε(u″ _ε(t)+A₁u_ε(t))+u′ _ε(t)+A₀u_ε(t)+B(u_ε(t)) =f_ε(t), t∈(0,T], u_ε(0)=u_0ε, u′_ε(0)=u_1ε, in the Hilbert space H as ε→0, where A₁, A₀ are two linear self-adjoint operators and B is a Lipschitzian operator. © 2011 - IOS Press and the authors. All rights reserved.

Cuvinte-cheie
a priori estimate, abstract second-order Cauchy problem, boundary layer function, singular perturbation

Cerif XML Export

<?xml version='1.0' encoding='utf-8'?>
<CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'>
<cfResPubl>
<cfResPublId>ibn-ResPubl-198805</cfResPublId>
<cfResPublDate>2011-08-01</cfResPublDate>
<cfStartPage>135</cfStartPage>
<cfISSN>0921-7134</cfISSN>
<cfURI>https://ibn.idsi.md/ro/vizualizare_articol/198805</cfURI>
<cfTitle cfLangCode='EN' cfTrans='o'>Convergence estimates for abstract second-order singularly perturbed Cauchy problems with Lipschitzian nonlinearities</cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>a priori estimate; abstract second-order Cauchy problem; boundary layer function; singular perturbation</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'><p>We study the behavior of solutions to the problem &epsilon;(u&Prime;&nbsp;<sub>&epsilon;</sub>(t)+A<sub>1</sub>u<sub>&epsilon;</sub>(t))+u&prime;&nbsp;<sub>&epsilon;</sub>(t)+A<sub>0</sub>u<sub>&epsilon;</sub>(t)+B(u<sub>&epsilon;</sub>(t)) =f<sub>&epsilon;</sub>(t), t&isin;(0,T], u<sub>&epsilon;</sub>(0)=u<sub>0&epsilon;</sub>, u&prime;<sub>&epsilon;</sub>(0)=u<sub>1&epsilon;</sub>, in the Hilbert space H as &epsilon;&rarr;0, where A<sub>1</sub>, A<sub>0</sub>&nbsp;are two linear self-adjoint operators and B is a Lipschitzian operator. &copy; 2011 - IOS Press and the authors. All rights reserved.</p></cfAbstr>
<cfResPubl_Class>
<cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId>
<cfStartDate>2011-08-01T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfResPubl_Class>
<cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId>
<cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId>
<cfStartDate>2011-08-01T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfPers_ResPubl>
<cfPersId>ibn-person-10557</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2011-08-01T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfPers_ResPubl>
<cfPersId>ibn-person-28577</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2011-08-01T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfFedId>
<cfFedIdId>ibn-doi-198805</cfFedIdId>
<cfFedId>10.3233/ASY-2011-1043</cfFedId>
<cfStartDate>2011-08-01T24:00:00</cfStartDate>
<cfFedId_Class>
<cfClassId>31d222b4-11e0-434b-b5ae-088119c51189</cfClassId>
<cfClassSchemeId>bccb3266-689d-4740-a039-c96594b4d916</cfClassSchemeId>
</cfFedId_Class>
<cfFedId_Srv>
<cfSrvId>5123451</cfSrvId>
<cfClassId>eda2b2e2-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>5a270628-f593-4ff4-a44a-95660c76e182</cfClassSchemeId>
</cfFedId_Srv>
</cfFedId>
</cfResPubl>
<cfPers>
<cfPersId>ibn-Pers-10557</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-10557-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2011-08-01T24:00:00</cfStartDate>
<cfFamilyNames>Perjan</cfFamilyNames>
<cfFirstNames>Andrei</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfPers>
<cfPersId>ibn-Pers-28577</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-28577-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2011-08-01T24:00:00</cfStartDate>
<cfFamilyNames>Rusu</cfFamilyNames>
<cfFirstNames>Galina</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfSrv>
<cfSrvId>5123451</cfSrvId>
<cfName cfLangCode='en' cfTrans='o'>CrossRef DOI prefix service</cfName>
<cfDescr cfLangCode='en' cfTrans='o'>The service of issuing DOI prefixes to publishers</cfDescr>
<cfKeyw cfLangCode='en' cfTrans='o'>persistent identifier; Digital Object Identifier</cfKeyw>
</cfSrv>
</CERIF>