Sufficient conditions under which the solutions of general parabolic initial-boundaryvalue problems are classical
We establish new sufficient conditions under which the generalized solutions of initial-boundary-value problems for the linear parabolic differential equations of any order with complex-valued coefficients are classical. These conditions are formulated in the terms of belonging of the right-hand sid...
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| Date: | 2016 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2016
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1938 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We establish new sufficient conditions under which the generalized solutions of initial-boundary-value problems for the
linear parabolic differential equations of any order with complex-valued coefficients are classical. These conditions are
formulated in the terms of belonging of the right-hand sides of this problem to certain anisotropic H¨ormander spaces. In
the definition of classical solution, its continuity on the line connecting the lateral surface with the base of the cylinder (in
which the problem is considered) is not required. |
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