Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems
We are interested in the existence of distributional solutions for two types of nonlinear evolution problems, whose models are (1.1) and (1.2) below. In the first one the nonlinear reaction term depends on the solution with a slightly superlinear growth. In the second one we consider a first order t...
Збережено в:
| Дата: | 2004 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2004
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| Назва видання: | Український математичний вісник |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/124629 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems / A. Dall'Aglio, D. Giachett, S. Segura de Leon // Український математичний вісник. — 2004. — Т. 1, № 4. — С. 518-531. — Бібліогр.: 13 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We are interested in the existence of distributional solutions for two types of nonlinear evolution problems, whose models are (1.1) and (1.2) below. In the first one the nonlinear reaction term depends on the solution with a slightly superlinear growth. In the second one we consider a first order term depending also on the gradient of the solution in a quadratic way. The two problems are strictly related from the point of view of the a priori estimates we can obtain on their solutions. We point out that no boundedness is assumed on the data of the problems. This implies that the methods involving sub/super-solutions do not apply, and we have to use some convenient test-function to prove the a priori estimates. |
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