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...
Збережено в:
| Дата: | 2000 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2000
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156146 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems / L.R. Berrone // Український математичний журнал. — 2000. — Т. 52, № 2. — С. 165–182. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
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