Kopachevsky, N. D. and Mennicken, Reinhard and Pashkova, J. S. and Tretter, C. (2004) Complete second order linear differential operator equations in Hilbert space and applications in hydrodynamics. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 356 (12). pp. 4737-4766. ISSN 0002-9947, 1088-6850
Full text not available from this repository. (Request a copy)Abstract
We study the Cauchy problem for a complete second order linear differential operator equation in a Hilbert space H of the form d(2)u/dt(2) + (F+iK) du/dt + Bu=f, u(0)=u(0), u'(0)=u(1). Problems of this kind arise, e. g., in hydrodynamics where the coefficients F, K, and B are unbounded selfadjoint operators. It is assumed that F is the dominating operator in the Cauchy problem above, i.e., D(F) subset of D(B); D(F) subset of D(K). We also suppose that F and B are bounded from below, but the operator coefficients are not assumed to commute. The main results concern the existence of strong solutions to the stated Cauchy problem and applications of these results to the Cauchy problem associated with small motions of some hydrodynamical systems.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MATRICES; OSCILLATIONS; SPECTRUM; block operator matrix; differential equation in Hilbert space; evolution problem; Navier-Stokes equations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 27 Jul 2021 08:55 |
| Last Modified: | 27 Jul 2021 08:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/38279 |
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