Well-posedness of the cauchy problem for complete second-order operator-differential equations
For the equation y″(t)+Ay′(t)+By(t)=0, where A and B are arbitrary commuting normal operators in a Hilbert space H, we obtain a necessary and sufficient condition for well-posedness of the Cauchy problem in the space of initial data D(B)×(D(A)∩D(|B|1/2)) and for weak well-posedness of the Cauchy pro...
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5272 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | For the equation y″(t)+Ay′(t)+By(t)=0, where A and B are arbitrary commuting normal operators in a Hilbert space H, we obtain a necessary and sufficient condition for well-posedness of the Cauchy problem in the space of initial data D(B)×(D(A)∩D(|B|1/2)) and for weak well-posedness of the Cauchy problem in H×H_(|A|+|B|1/2+1). This condition is expressed in terms of location of the joint spectrum of the operators A and B in C 2. In terms of location of the spectrum of the operator pencil z 2+Az+B in C 1, such a condition cannot be written. |
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