01.01.02 (Differential equations, dynamical systems, and optimal control)
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.
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.
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.
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.
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
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
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; Dokl. Math., 48:3 (1994), 602–605
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; Dokl. Math., 47:2 (1993), 310–314
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; Dokl. Math., 46:1 (1993), 169–173
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; Dokl. Math., 45:2 (1992), 360–365
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; Dokl. Math., 43:2 (1991), 366–370
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; Dokl. Math., 43:2 (1991), 325–328
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; Dokl. Math., 40:3 (1990), 610–613
M. Imanaliev, Yu. A. Ved', “A first-order partial differential equation with an integral coefficient”, Differ. Uravn., 25:3 (1989), 465–477; Differ. Equ., 25:3 (1989), 325–335
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; Dokl. Math., 38:3 (1989), 560–563
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
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
M. Imanaliev, B. V. Khvedelidze, T. G. Gegelia, A. A. Babaev, A. I. Botashev, “Integral equations”, Differ. Uravn., 18:12 (1982), 2050–2069
M. Imanaliev, P. S. Pankov, “Generalized solution of an integral equation of the first kind”, Differ. Uravn., 16:5 (1980), 937–940
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
M. Imanaliev, P. S. Pankov, “Всесоюзная конференция «Асимптотика – 91»”, Differ. Uravn., 28:6 (1992), 1095
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