Systems parabolic in Petrovskii's sense in Hörmander spaces
We study a general parabolic initial-boundary-value problem for systems parabolic in Petrovskii’s sense with zero initial Cauchy data in some anisotropic H¨ormander inner-product spaces.We prove that the operators corresponding to this problem are isomorphisms between the appropriate H¨ormander spac...
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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1702 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study a general parabolic initial-boundary-value problem for systems parabolic in Petrovskii’s sense with zero initial
Cauchy data in some anisotropic H¨ormander inner-product spaces.We prove that the operators corresponding to this problem
are isomorphisms between the appropriate H¨ormander spaces. As an application of this result, we establish a theorem on
the local increase in regularity of solutions of the problem. We also obtain new sufficient conditions of continuity for the
generalized partial derivatives of a given order of a chosen component of the solution. |
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