Continuity with respect to initial data and absolute-continuity approach to the first-order regularity of nonlinear diffusions on noncompact manifolds
We study the dependence with respect to the initial data for solutions of diffusion equations with globally non-Lipschitz coefficients on noncompact manifolds. Though the metric distance may be not everywhere twice differentiable, we show that under some monotonicity conditions on coefficients and...
Збережено в:
Видавець: | Інститут математики НАН України |
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Дата: | 2008 |
Автори: | , |
Формат: | Стаття |
Мова: | English |
Опубліковано: |
Інститут математики НАН України
2008
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Назва видання: | Український математичний журнал |
Теми: | |
Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/164759 |
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Цитувати: | Continuity with respect to initial data and absolute-continuity approach to the first-order regularity of nonlinear diffusions on noncompact manifolds / A.Val. Antoniouk, A.Vict. Antoniouk // Український математичний журнал. — 2008. — Т. 60, № 10. — С. 1299–1316. — Бібліогр.: 14 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of UkraineРезюме: | We study the dependence with respect to the initial data for solutions of diffusion equations with globally
non-Lipschitz coefficients on noncompact manifolds. Though the metric distance may be not everywhere
twice differentiable, we show that under some monotonicity conditions on coefficients and curvature of
manifold there are estimates exponential in time on the continuity of diffusion process with respect to the
initial data.
These estimates are combined with methods of the theory of absolutely continuous functions to
achieve the first-order regularity of solutions with respect to the initial data. The suggested approach
neither appeals to the local stopping time arguments, nor applies the exponential mappings on tangent
space, nor uses embeddings of manifold to linear spaces of higher dimensions. |
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