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Falaleev, Mihail Valentinovich

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Total publications: 28
Scientific articles: 25

Number of views:
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Abstract pages:4572
Full texts:1824
References:466
Professor
Doctor of physico-mathematical sciences (1988)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 19.02.1961
E-mail:
Keywords: differential equations in Banach spaces; generalized functions; integral equations of the 1-ht kind; theory of semigroups of operators.

Subject:

In several papers the problem of generalized solutions construction of degenerated differential and integral equations in Banach spaces was investigated. In the last of papers (SMJ, 2000, v. 41, no. 5) this problem was solved by fundamental operator construction for some classes of differential, integral and integro-differential operators. Some papers concern the development of analytical theory of the systems of Volterra integral equations, used in the construction of logariphm-power solutions of these systems. These ideas allow to construct the similar solutions for the integral equations with the singularities. For the integral Volterra equation of the first kind the problem of correct statement and construction of generalized solutions in the Schwarz distribution class with the left bounded carrier was solved.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1984 (department of theory of functions and functional analysis). Ph.D. thesis was defended in 1988. A list of my works contains more than 40 titles.

   
Main publications:
  • Falaleev M. V. Asymptotic expansions of continuous solutions of system of Volterra integral equations of the first kind // International symposium on computerized tomography. Novosibirsk, Russia, August 10–14, 1993. Amsterdam, Nord-Holl, 1994, p. 155–157.

http://www.mathnet.ru/eng/person17902
List of publications on Google Scholar
https://zbmath.org/authors/?q=ai:falaleev.mikhail-valentinovich
https://mathscinet.ams.org/mathscinet/MRAuthorID/255142

Publications in Math-Net.Ru
2020
1. M. V. Falaleev, “On solvability in the class of distributions of degenerate integro-differential equations in Banach spaces”, The Bulletin of Irkutsk State University. Series Mathematics, 34 (2020),  77–92  mathnet
2. M. V. Falaleev, “Generalized solutions of degenerate integro-differential equations in Banach spaces”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 183 (2020),  139–151  mathnet  mathscinet
3. M. V. Falaleev, “Fundamental operator functions of integro-differential operators under spectral or polynomial boundedness”, Ufimsk. Mat. Zh., 12:2 (2020),  55–70  mathnet; Ufa Math. J., 12:2 (2020), 56–71  isi
2017
4. M. V. Falaleev, “Fundamental operator-valued functions of singular integrodifferential operators in Banach spaces”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 132 (2017),  127–130  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 230:5 (2018), 782–785  scopus
2016
5. M. V. Falaleev, “Degenerate integro-differential equations of convolution type in Banach spaces”, The Bulletin of Irkutsk State University. Series Mathematics, 17 (2016),  77–85  mathnet
2013
6. M. V. Falaleev, “Singular integro-differential equations of the special type in Banach spaces and it’s applications”, The Bulletin of Irkutsk State University. Series Mathematics, 6:4 (2013),  128–137  mathnet
7. M. V. Falaleev, “Linear Models in Theory of Viscoelasticity of Sobolev Type”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:4 (2013),  101–107  mathnet
2012
8. M. V. Falaleev, “Integro-differential equations with Fredholm operator by the derivative of the higest order in Banach spaces and it's applications”, The Bulletin of Irkutsk State University. Series Mathematics, 5:2 (2012),  90–102  mathnet
9. M. V. Falaleev, S. S. Orlov, “Generalized solutions of singular integro-differential equations in Banach spaces and their applications”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:4 (2012),  286–297  mathnet  elib
10. N. A. Sidorov, M. V. Falaleev, “Continuous and generalized solutions of singular integro-differential equations in Banach spaces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, 11,  62–74  mathnet
2011
11. N. A. Sidorov, M. V. Falaleev, O. A. Romanova, “Vladilen Aleksandrovich Trenogin”, The Bulletin of Irkutsk State University. Series Mathematics, 4:3 (2011),  171–172  mathnet
12. M. V. Falaleev, S. S. Orlov, “Integro-differential equations with degeneration in Banach spaces and it's applications in mathematical theory of elasticity”, The Bulletin of Irkutsk State University. Series Mathematics, 4:1 (2011),  118–134  mathnet
13. M. V. Falaleev, S. S. Orlov, “Degenerate integro-differential operators in Banach spaces and their applications”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, 10,  68–79  mathnet  mathscinet; Russian Math. (Iz. VUZ), 55:10 (2011), 59–69  scopus
14. M. V. Falaleev, S. S. Orlov, “Degenerated integro-differential equations of special kind in Banach spaces and it's applications”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2011, 7,  100–110  mathnet
2010
15. M. V. Falaleev, “Degenerated abstract problem of prediction-control in Banach spaces”, The Bulletin of Irkutsk State University. Series Mathematics, 3:1 (2010),  126–132  mathnet
16. M. V. Falaleev, A. V. Krasnik, S. S. Orlov, “Degenerate high-order differential equations of a special kind in Banach spaces and their applications”, Sib. Zh. Ind. Mat., 13:3 (2010),  126–139  mathnet  mathscinet
2008
17. M. V. Falaleev, O. V. Korobova, “Systems of degenerate differential equations in Banach spaces”, Sibirsk. Mat. Zh., 49:4 (2008),  916–927  mathnet  mathscinet  zmath  elib; Siberian Math. J., 49:4 (2008), 734–743  isi  elib  scopus
2006
18. M. V. Falaleev, E. Yu. Grazhdantseva, “Fundamental operator functions of singular differential operators under spectral boundedness conditions”, Differ. Uravn., 42:6 (2006),  769–774  mathnet  mathscinet; Differ. Equ., 42:6 (2006), 819–825
19. M. V. Falaleev, “Fundamental operator functions of singular differential operators under sectoriality and radiality conditions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2006, 10,  68–75  mathnet  mathscinet  elib; Russian Math. (Iz. VUZ), 50:10 (2006), 64–71
2005
20. M. V. Falaleev, N. A. Sidorov, D. N. Sidorov, “Generalized solutions of Volterra integral equations of the first kind”, Lobachevskii J. Math., 20 (2005),  47–57  mathnet  mathscinet  zmath
21. M. V. Falaleev, N. A. Sidorov, “Continuous and generalized solutions of singular partial differential equations”, Lobachevskii J. Math., 20 (2005),  31–45  mathnet  mathscinet  zmath  elib
22. M. V. Falaleev, E. Yu. Grazhdantseva, “Fundamental operator-functions of degenerate differential and difference-differential operators in Banach spaces which have a Noether operator in the principal part”, Sibirsk. Mat. Zh., 46:6 (2005),  1393–1406  mathnet  mathscinet  zmath  elib; Siberian Math. J., 46:6 (2005), 1123–1134  isi
2000
23. M. V. Falaleev, “Fundamental operator-functions of singular differential operators in Banach spaces”, Sibirsk. Mat. Zh., 41:5 (2000),  1167–1182  mathnet  mathscinet  zmath; Siberian Math. J., 41:5 (2000), 960–973  isi
1999
24. M. V. Falaleev, “Задача Коши для вырожденных интегро-дифференциальных уравнений в банаховых пространствах”, Vestnik Chelyabinsk. Gos. Univ., 1999, 5,  126–136  mathnet
1987
25. N. A. Sidorov, M. V. Falaleev, “Generalized solution of differential equations with a Fredholm operator at the derivative”, Differ. Uravn., 23:4 (1987),  726–728  mathnet  zmath

2020
26. M. V. Falaleev, O. A. Romanova, A. V. Sinitsyn, A. I. Dreglea, R. Yu. Leont'ev, D. N. Sidorov, “On the occasion of the 80th birthday of professor N. A. Sidorov”, The Bulletin of Irkutsk State University. Series Mathematics, 32 (2020),  134–143  mathnet
2018
27. N. A. Sidorov, O. A. Romanova, M. V. Falaleev, D. N. Sidorov, V. K. Gorbunov, A. I. Dreglea, “In the memory of professor Boris Vladimirovich Loginov”, The Bulletin of Irkutsk State University. Series Mathematics, 23 (2018),  96–99  mathnet
2013
28. N. A. Sidorov, M. V. Falaleev, “In the memory of Trenogin Vladilen Aleksandrovich”, The Bulletin of Irkutsk State University. Series Mathematics, 6:4 (2013),  138–140  mathnet

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