Mutual spectrum of commutating conjugate operators and correctness and stability criteria for differential-operator equations
Tests are established for the propriety of the Cauchy problem, the stability, stabilization, asymptotic stability, and exponential stability for the equation $y'' + By' + By = 0, t \in [0, +\infty)$, where $A$ and $B$ are arbitrary commuting self-adjoint operators on a sep...
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| Date: | 1991 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1991
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9623 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | Tests are established for the propriety of the Cauchy problem, the stability, stabilization, asymptotic stability, and exponential stability for the equation $y'' + By' + By = 0, t \in [0, +\infty)$, where $A$ and $B$ are arbitrary commuting self-adjoint operators on a separable Hilbert space. For this, in terms of the arrangement in $R^2$ of the joint spectrum of $A$ and $B$ tests are obtained for $B$ to be subordinate (strongly subordinate, equivalent) to $A$. The results on propriety and stability are illustrated by the example of model partial differential equations. |
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