Well-defined solvability and spectral analysis of abstract hyperbolic integrodifferential equations |
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Authors: | V V Vlasov N A Rautian |
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Institution: | 1.Moscow State University,Moscow,Russia;2.Plekhanov Russian State University of Economics,Moscow,Russia |
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Abstract: | The authors study integrodifferential equations in Hilbert space. The coefficients of the equations are unbounded and the
principal part is an abstract hyperbolic equation perturbed by terms with Volterra integral operators. Such equations can
be regarded as an abstract generalization of the Gurtin–Pipkin integrodifferential equation that describes heat transfer in
materials with memory and has a number of other applications. Well-defined solvability of initial boundary value problems
for such equations is established in weighted Sobolev spaces on the positive semi-axis. The authors examine spectral problems
for operator-valued functions representing the symbols of the said equations and study the spectrum of the abstract Gurtin–Pipkin
integrodifferential equation. |
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Keywords: | |
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