Well-posedness and spectral analysis of integrodifferential equations of hereditary mechanics
V. V. Vlasovab, N. A. Rautianab
a Lomonosov Moscow State University
b Moscow Center of Fundamental and Applied Mathematics, Moscow, 119991 Russia
The well-posedness of initial value problems for abstract integrodifferential equations with unbounded operator coefficients in Hilbert spaces is studied, and spectral analysis of the operator functions that are the symbols of these equations is performed. The equations under consideration are an abstract form of linear partial integrodifferential equations arising in viscoelasticity theory, which have a number of other important applications. Results concerning the well-posedness of these integrodifferential equations in weighted Sobolev spaces of vector functions defined on the positive half-line with values in a Hilbert space are obtained. The localization and structure of the spectrum of the operator functions that are the symbols of these equations are established.
integrodifferential equations, operator functions, spectral analysis.
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1322–1330
V. V. Vlasov, N. A. Rautian, “Well-posedness and spectral analysis of integrodifferential equations of hereditary mechanics”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1367–1376; Comput. Math. Math. Phys., 60:8 (2020), 1322–1330
Citation in format AMSBIB
\by V.~V.~Vlasov, N.~A.~Rautian
\paper Well-posedness and spectral analysis of integrodifferential equations of hereditary mechanics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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