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Spectral operators generated by damped hyperbolic equations. (English) Zbl 0912.47016
The author presents results on the spectral analysis of two nonselfadjoint operators which are the dynamics generators for systems governed by hyperbolic equations containing dissipative terms, namely, the nonhomogeneous damped string and the 3-dimensional damped wave equation with spacially nonhomogeneous spherically symmetric coefficients. Nonselfadjoint boundary conditions are imposed at the ends of a finite interval or on a sphere centered at the origin, respectively. It is shown that these operators are spectral in the sense of N. Dunford using the fact that the systems of root vectors form a Riesz basis in the corresponding energy spaces. Asymptotics of the spectra are obtained and results are stated on the property of the Riesz bases for the nonselfadjoint operator pencils associated with these operators.

47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
35L10 Second-order hyperbolic equations
Full Text: DOI
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