On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator
For the evolution equation 𝑦(𝑡)=𝐴𝑦(𝑡) with a scalar type spectral operator 𝐴 in a Banach space, conditions on 𝐴 are found that are necessary and sufficient for all weak solutions of the equation on [0,∞) to be strongly infinite differentiable on [0,∞) or [0,∞). Certain effects of smoothness improve...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/825951 |
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| _version_ | 1849407566224818176 |
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| author | Marat V. Markin |
| author_facet | Marat V. Markin |
| author_sort | Marat V. Markin |
| collection | DOAJ |
| description | For the evolution equation 𝑦(𝑡)=𝐴𝑦(𝑡) with a scalar type spectral operator 𝐴 in a Banach space, conditions on 𝐴 are found that are necessary and sufficient for all weak solutions of the equation on [0,∞) to be strongly infinite differentiable on [0,∞) or [0,∞). Certain effects of smoothness improvement of the weak solutions are analyzed. |
| format | Article |
| id | doaj-art-48ab14d2b71747a7ae18558affdba1dc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-48ab14d2b71747a7ae18558affdba1dc2025-08-20T03:36:01ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/825951825951On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral OperatorMarat V. Markin0Department of Partial Differential Equations, Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchekivs'ka Street, 01601 Kiev, UkraineFor the evolution equation 𝑦(𝑡)=𝐴𝑦(𝑡) with a scalar type spectral operator 𝐴 in a Banach space, conditions on 𝐴 are found that are necessary and sufficient for all weak solutions of the equation on [0,∞) to be strongly infinite differentiable on [0,∞) or [0,∞). Certain effects of smoothness improvement of the weak solutions are analyzed.http://dx.doi.org/10.1155/2011/825951 |
| spellingShingle | Marat V. Markin On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator International Journal of Mathematics and Mathematical Sciences |
| title | On the Differentiability
of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator |
| title_full | On the Differentiability
of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator |
| title_fullStr | On the Differentiability
of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator |
| title_full_unstemmed | On the Differentiability
of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator |
| title_short | On the Differentiability
of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator |
| title_sort | on the differentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator |
| url | http://dx.doi.org/10.1155/2011/825951 |
| work_keys_str_mv | AT maratvmarkin onthedifferentiabilityofweaksolutionsofanabstractevolutionequationwithascalartypespectraloperator |