Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems
Sufficient conditions are obtained for a Volterra integral equation whose kernel depends on an increasing parameter a to admit an approximation of the identity with respect to a in the form of a resolvent kernel. In this case, the solution of the integral equation tends to zero as a tends to infinit...
Saved in:
| Date: | 2000 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2000
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4406 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865791535904194560 |
|---|---|
| author | Berrone, L. R Берроне, Л. Р. |
| author_facet | Berrone, L. R Берроне, Л. Р. |
| author_institution_txt_mv | [
{
"author": "L. R Berrone",
"institution": null
}
] |
| author_sort | Berrone, L. R |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:28:32Z |
| description | Sufficient conditions are obtained for a Volterra integral equation whose kernel depends on an increasing parameter a to admit an approximation of the identity with respect to a in the form of a resolvent kernel. In this case, the solution of the integral equation tends to zero as a tends to infinity, and we establish estimates of this convergence in L. These results are used for obtaining estimates of the convergence of linear heat-transfer boundary conditions to Dirichlet ones as the heat-transfer coefficient tends to infinity. |
| first_indexed | 2026-03-24T02:58:34Z |
| format | Article |
| fulltext |
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
0030
0031
0032
0033
0034
0035
|
| id | umjimathkievua-article-4406 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:58:34Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ee/9c181ac599eaedba3dedc6ba0c9d6fee.pdf |
| spelling | umjimathkievua-article-44062020-03-18T20:28:32Z Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems Резольвентні ядра, що є апроксимацією одиниці, та лінійні задачі теплообміну Berrone, L. R Берроне, Л. Р. Sufficient conditions are obtained for a Volterra integral equation whose kernel depends on an increasing parameter a to admit an approximation of the identity with respect to a in the form of a resolvent kernel. In this case, the solution of the integral equation tends to zero as a tends to infinity, and we establish estimates of this convergence in L. These results are used for obtaining estimates of the convergence of linear heat-transfer boundary conditions to Dirichlet ones as the heat-transfer coefficient tends to infinity. Отримані достатні умови, при яких інтегральне рівняння Вольтерра з ядром, що залежить від зростаючого параметра $\alpha$, допускає наближення одиниці відносно $\alpha$ у вигляді резольвентного ядра. У цьому випадку розв'язок інгегрального рівняння прямує до нуля, коли а прямує до нескінченності, і отримані оцінки цієї збіжності в $L^{\infty}$. За допомогою цих результатів одержані оцінки збіжності лінійних граничних умов Діріхле, коли коефіцієнт теплообміну прямує до нескінченності. Institute of Mathematics, NAS of Ukraine 2000-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4406 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 2 (2000); 165-182 Український математичний журнал; Том 52 № 2 (2000); 165-182 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/4406/5516 https://umj.imath.kiev.ua/index.php/umj/article/view/4406/5517 Copyright (c) 2000 Berrone L. R |
| spellingShingle | Berrone, L. R Берроне, Л. Р. Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems |
| title | Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems |
| title_alt | Резольвентні ядра, що є апроксимацією одиниці, та лінійні задачі теплообміну |
| title_full | Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems |
| title_fullStr | Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems |
| title_full_unstemmed | Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems |
| title_short | Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems |
| title_sort | resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4406 |
| work_keys_str_mv | AT berronelr resolventkernelsthatconstituteanapproximationoftheidentityandlinearheattransferproblems AT berronelr resolventkernelsthatconstituteanapproximationoftheidentityandlinearheattransferproblems AT berronelr rezolʹventníâdraŝoêaproksimacíêûodinicítalíníjnízadačíteploobmínu AT berronelr rezolʹventníâdraŝoêaproksimacíêûodinicítalíníjnízadačíteploobmínu |