Integral manifolds and exponential splitting of linear parabolic equations with rapidly varying coefficients
We study linear parabolic equations with rapidly varying coefficients. It is assumed that the averaged equation corresponding to the source equation admits exponential splitting. We establish conditions under which the source equation also admits exponential splitting. It is shown that integral mani...
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| Дата: | 1995 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1995
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5553 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We study linear parabolic equations with rapidly varying coefficients. It is assumed that the averaged equation corresponding to the source equation admits exponential splitting. We establish conditions under which the source equation also admits exponential splitting. It is shown that integral manifolds play an important role in constructing transformations that split the equations under consideration. To prove the existence of integral manifolds, we apply Zhikov's results on the justification of the averaging method for linear parabolic equations. |
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