Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients
Below we demonstrate how the C^∞-regular properties of heat dynamics with non-unit nonlinear diffusion coefficient can be studied. We consider an infinite dimensional model, describing evolution of unbounded lattice spins R^Z^d. As a main step we provide a construction of corresponding variational p...
Збережено в:
| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2007
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/10116 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients / A.Val. Antoniouk, A.Vict. Antoniouk // Нелинейные граничные задачи. — 2007. — Т. 17. — С. 101-129. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Below we demonstrate how the C^∞-regular properties of heat dynamics with non-unit nonlinear diffusion coefficient can be studied. We consider an infinite dimensional model, describing evolution of unbounded lattice spins R^Z^d. As a main step we provide a construction of corresponding variational processes in ℓp(c) spaces with growing weights ck ~ e^a|k|, k belongs Z^d.
Developing the approach of nonlinear estimates on variations, we find sufficient conditions on the nonlinear coefficients of differential equation that lead to C^∞-regularity of solutions with respect to the initial data and C^∞-regularity of corresponding heat semigroup. |
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