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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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2007
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| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/10116 |
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| Summary: | 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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