Nonlinear-estimate approach to the regularity of infinite-dimensional parabolic problems
We show how the use of nonlinear symmetries of higher-order derivatives allows one to study the regularity of solutions of nonlinear differential equations in the case where the classical Cauchy-Liouville-Picard scheme is not applicable. In particular, we obtain nonlinear estimates for the boundedne...
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| Date: | 2006 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2006
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/164994 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Nonlinear-estimate approach to the regularity of infinite-dimensional parabolic problems / A.Val. Antoniouk, A.Vict. Antoniouk // Український математичний журнал. — 2006. — Т. 58, № 5. — С. 579–596. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We show how the use of nonlinear symmetries of higher-order derivatives allows one to study the regularity of solutions of nonlinear differential equations in the case where the classical Cauchy-Liouville-Picard scheme is not applicable. In particular, we obtain nonlinear estimates for the boundedness and continuity of variations with respect to initial data and discuss their applications to the dynamics of unbounded lattice Gibbs models. |
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