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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 8, Pages 1367–1376 (Mi zvmmf11117)  

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

Abstract: 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.

Key words: integrodifferential equations, operator functions, spectral analysis.

Funding Agency Grant Number
Russian Foundation for Basic Research 20-01-00288
This study was supported by the Russian Foundation for Basic Research, project no. 20-01-00288.


DOI: https://doi.org/10.31857/S0044466920080153


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1322–1330

Bibliographic databases:

UDC: 517.968.72
Received: 07.05.2019
Revised: 11.07.2019
Accepted:09.04.2020

Citation: 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
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\pages 1367--1376
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