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Properties of solutions of integro-differential equations arising in heat and mass transfer theory


Authors: V. V. Vlasov and N. A. Rautian
Translated by: V. E. Nazaikinskii
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 75 (2014), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2014, 185-204
MSC (2010): Primary 47G20; Secondary 34K30, 47A56, 34K12
DOI: https://doi.org/10.1090/S0077-1554-2014-00231-4
Published electronically: November 5, 2014
MathSciNet review: 3308609
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Abstract: The aim of the present paper is to study the asymptotic behavior of solutions of integro-differential equations on the basis of spectral analysis of their symbols. To this end, we obtain representations of strong solutions of these equations in the form of a sum of terms corresponding to the real and nonreal parts of the spectrum of the operator functions that are the symbols of these equations. These representations are new for the class of integro-differential equations considered in the paper.


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Additional Information

V. V. Vlasov
Affiliation: Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
Email: vikmont@yandex.ru

N. A. Rautian
Affiliation: Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
Email: nraytian@mail.ru

DOI: https://doi.org/10.1090/S0077-1554-2014-00231-4
Keywords: Integro-differential equation, operator function, spectral analysis
Published electronically: November 5, 2014
Additional Notes: The first author was supported by RFBR grants no. 14-01-00349, 13-01-12476-ofi-m-2013, and 13-01-00384.
The second author was supported by RFBR grants no. 14-01-00349 and 13-01-00384.
Article copyright: © Copyright 2014 American Mathematical Society