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Imanaliev, Murzabek

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Total publications: 18
Scientific articles: 16

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Full texts:362
Corresponding member of RAS
Professor
Doctor of physico-mathematical sciences (1965)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 13.09.1931
E-mail:
Keywords: differential equations; integral equations; integro-differential equations; equations in partial derivatives; asymptotical methods; classes of singular-perturbed equations and systems; periodical and nearly periodical solutions; incorrect problems; uniqueness, existence and stability; existence and approximation of generalized integral equations.

Subject:

Has shown the principal difference of integro-differential equations by perturbation theory under derivatives of corespondent theory of differential equations and created general asymptotical method for searching of wide class of singular-perturbed equations and systems. Developed the theory of branching of periodical, nearly periodical and bounded solutions of differential and integro-differential perturbed equations under highest derivative. Developed the theory of linear and nonlinear integral equations of first class of equations in continuous on final interval space, offered the methods of regularization of solutions of these equations, based on methods of theory of singular-perturbed systems. Developed the method of additional argument, the main idea of which is that the initial problem by inserting the additional variable is reduced to convenient to searching system of integral equations.

Biography

Graduated from Faculty of Physics and Mathematics of Kyrgyz State University (KSU) in 1953. Ph.D. thesis was defended in 1957. D.Sc. Thesis was defended in 1965. A list of my works contains more than 200 titles. Since 1966 I have led the research seminar of mathematicians at the Institute of Mathematics of National Academy of Sciences.

Member of Academy of Sciences of Kyrgyz Republic since 1979. Member-Correspondent of Russian Academy of Sciences, Russian Federation since 1981. I was awarded the Order of Red Labor in 1981, Order of Manas in 1999. Honorable Gold Medal of President of Kyrgyz Republic for distinguished scientific achievements in XX century in 2001.

   
Main publications:
  • Asymptotical Methods in Theory of singular-perturbed integer-differential systems, Ilim, Frunze, 1972.
  • Oscillations and stability of solution of singular-perturbed integer-differential systems, Ilim, Frunze, 1974.

http://www.mathnet.ru/eng/person17600
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1995
1. M. Imanaliev, P. S. Pankov, T. M. Imanaliev, “On the theory of nonlinear partial differential equations of Korteweg-de Vries type”, Dokl. Akad. Nauk, 342:1 (1995),  17–19  mathnet  mathscinet  zmath
1994
2. M. Imanaliev, R. K. Khanov, Sh. D. Shamgunov, “Interaction of load carrying waves in elastic medium with layered obstacles”, Dokl. Akad. Nauk, 335:2 (1994),  167–169  mathnet
1993
3. M. Imanaliev, P. S. Pankov, “The phenomenon of a withdrawing boundary layer in the theory of singularly perturbed ordinary differential equations”, Dokl. Akad. Nauk, 333:5 (1993),  575–577  mathnet  mathscinet  zmath; Dokl. Math., 48:3 (1994), 602–605
4. M. Imanaliev, S. N. Alekseenko, “On the theory of nonlinear equations with a differential operator that is of total derivative with respect to time type”, Dokl. Akad. Nauk, 329:5 (1993),  543–546  mathnet  mathscinet  zmath; Dokl. Math., 47:2 (1993), 310–314
1992
5. M. Imanaliev, S. N. Alekseenko, “On the theory of systems of nonlinear integropartial differential equations of Whitham type”, Dokl. Akad. Nauk, 325:6 (1992),  1111–1115  mathnet  mathscinet  zmath; Dokl. Math., 46:1 (1993), 169–173
6. M. Imanaliev, S. N. Alekseenko, “On the theory of nonlinear integro-partial differential equations of Whitham type”, Dokl. Akad. Nauk, 323:3 (1992),  410–414  mathnet  mathscinet  zmath; Dokl. Math., 45:2 (1992), 360–365
1991
7. M. Imanaliev, S. Sharipov, “The blow-up phenomenon in the theory of integral equations of Volterra type of the first kind”, Dokl. Akad. Nauk SSSR, 317:2 (1991),  284–288  mathnet  mathscinet  zmath; Dokl. Math., 43:2 (1991), 366–370
8. M. Imanaliev, A. Asanov, “Solutions of systems of nonlinear two-dimensional Volterra integral equations of the first kind”, Dokl. Akad. Nauk SSSR, 317:1 (1991),  32–35  mathnet  mathscinet  zmath; Dokl. Math., 43:2 (1991), 325–328
1989
9. M. Imanaliev, A. Asanov, “Solutions of systems of nonlinear Volterra integral equations of the first kind”, Dokl. Akad. Nauk SSSR, 309:5 (1989),  1052–1055  mathnet  mathscinet  zmath; Dokl. Math., 40:3 (1990), 610–613
10. M. Imanaliev, Yu. A. Ved', “A first-order partial differential equation with an integral coefficient”, Differ. Uravn., 25:3 (1989),  465–477  mathnet  mathscinet; Differ. Equ., 25:3 (1989), 325–335
1988
11. M. Imanaliev, P. S. Pankov, “Singularly perturbed systems of ordinary differential equations in cases when “degenerate” systems have discontinuous solutions”, Dokl. Akad. Nauk SSSR, 303:3 (1988),  546–549  mathnet  mathscinet  zmath; Dokl. Math., 38:3 (1989), 560–563
1986
12. M. Imanaliev, P. S. Pankov, “The phenomenon of a rotating boundary layer in the theory of singularly perturbed systems of ordinary differential equations”, Dokl. Akad. Nauk SSSR, 289:3 (1986),  536–538  mathnet  mathscinet  zmath
1983
13. M. Imanaliev, P. S. Pankov, “On the question of determination of one-sided delta functions in a complex domain”, Differ. Uravn., 19:5 (1983),  893–896  mathnet  mathscinet  zmath
1982
14. M. Imanaliev, B. V. Khvedelidze, T. G. Gegelia, A. A. Babaev, A. I. Botashev, “Integral equations”, Differ. Uravn., 18:12 (1982),  2050–2069  mathnet  mathscinet
1980
15. M. Imanaliev, P. S. Pankov, “Generalized solution of an integral equation of the first kind”, Differ. Uravn., 16:5 (1980),  937–940  mathnet  mathscinet  zmath
1967
16. N. Kh. Bagirova, A. B. Vasil'eva, M. Imanaliev, “A question on the asymptotic solution of an optimal control problem”, Differ. Uravn., 3:11 (1967),  1895–1902  mathnet  mathscinet  zmath

1992
17. M. Imanaliev, P. S. Pankov, “Всесоюзная конференция «Асимптотика – 91»”, Differ. Uravn., 28:6 (1992),  1095  mathnet
1982
18. A. A. Il'yushin, M. Imanaliev, N. M. Matveev, Yu. A. Mitropol'skii, “Aleksandr Nikolaevich Filatov (on the occasion of his fiftieth birthday)”, Differ. Uravn., 18:2 (1982),  360–362  mathnet  mathscinet  zmath

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