Functional Differential Equations; Boundary Value Problems for Elliptic Functional Differential Equations; Nonlocal Problems; Feller Semigroups; Parabolic Functional Differential Equations.
Subject:
1) Functional Differential Equations a. Uniqueness of unbounded oscillating solution for linear delay differential equation of the second order. Previously this problem was formulated as unsolved. b. Periodic solutions of nonlinear functional differential equations. c. Solvability and smoothness of generalized solutions of boundary value problems for functional differential equations.
2) Boundary Value Problems for Elliptic Functional Differential Equations a. Necessary and sufficient conditions for the Garding inequality. b. Solvability and spectral properties of boundary value problems for elliptic functional differential equations. c. Smoothness of generalized solutions.
3) Nonlocal Problems a. Solvability, spectral properties, and smoothness of generalized solutions of nonlocal elliptic boundary value problems. Previously this problem was formulated as unsolved. b. Connection between boundary value problems for elliptic differentialdifference equations and nonlocal elliptic boundary value problems. c. Spectral properties of ordinary differential operators with nonlocal integral conditions.
4) Feller Semigroups a. Existence of Feller semigroups and counterexamples of nonexistence of Feller semigroups in nontransversal case. Previously this problem was formulated as unsolved. b. Existence of Feller semigroups in transversal case.
5) Parabolic Functional Differential Equations a. Solvability and smoothness of generalized solutions of boundary value problems for linear parabolic differentialdifference equations. b. Bifurcation of periodic solutions for quasilinear parabolic functional differential equation.
Biography
(a) November 1987, the Steklov Institute of Mathematics, Moscow, Doctor of Sciences in Mathematics, dissertation "Nonlocal Elliptic Boundary Value Problems";
(b) February 1980, MAI, Ph.D. in Mathematics, dissertation "Boundary Value Problems for Elliptic Equations with Deviating Arguments in Higher Terms";
(c) March 1976, MAI, Master in Applied Mathematics.
1988 – up to now, Full Professor, Head of Department of Differential Equations in MAI. A list of my works contains more than 100 titles. Jointly with Professor G. A. Kamenskii I lead the research seminar at MAI on differential and functional differential equations.
Member of the Moscow Mathematical Society, Member of the American Mathematical Society, Member of Editorial Board of the International Journal "Functional Differential Equations", Member of Mathematical Working Group of European Society for Engineering Education, Member of Presidium of Mathematical Committee of the Russian Ministry for Education, Member of Committees on awarding Ph.D. degrees in the Moscow State University and the Moscow State Aviation Institute. In 1994 and in 1999 I organized the International Conferences on Differential and Functional Differential Equations in Moscow.
A. Sh. Adkhamova, A. L. Skubachevskii, “Damping problem for control system with delay with different number of inputs and outputs”, CMFD, 70:2 (2024), 189–200
2.
V. V. Akhlynina, A. L. Skubachevskii, “Third mixed boundary-value problem for strongly elliptic differential-difference equations”, Uspekhi Mat. Nauk, 79:4(478) (2024), 175–176; Russian Math. Surveys, 79:4 (2024), 730–732
2023
3.
Yu. O. Belyaeva, A. L. Skubachevskii, “On global weak solutions of the Vlasov–Poisson equations with external magnetic field”, CMFD, 69:3 (2023), 383–398
4.
R. Yu. Vorotnikov, A. L. Skubachevskii, “Smoothness of Generalized Eigenfunctions of Differential–Difference Operators on a Finite Interval”, Mat. Zametki, 114:5 (2023), 679–701; Math. Notes, 114:5 (2023), 1002–1020
A. L. Skubachevskii, N. O. Ivanov, “Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients on Intervals of Noninteger Length”, Mat. Zametki, 111:6 (2022), 873–886; Math. Notes, 111:6 (2022), 913–924
J. Batt, E. Jörn, A. L. Skubachevskii, “Three-dimensional stationary spherically symmetric stellar dynamic models depending on the local energy”, Zh. Vychisl. Mat. Mat. Fiz., 62:9 (2022), 1491–1521; Comput. Math. Math. Phys., 62:9 (2022), 1455–1485
2021
7.
A. L. Skubachevskii, N. O. Ivanov, “On generalized solutions of the second boundary-value problem for differential-difference equations with variable coefficients”, CMFD, 67:3 (2021), 576–595
A. L. Skubachevskii, N. O. Ivanov, “The second boundary value problem for differential-difference equations”, Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021), 74–77; Dokl. Math., 104:2 (2021), 282–284
J. Batt, E. Jörn, A. L. Skubachevskii, “Stationary spherically symmetric solutions of the Vlasov–Poisson system in the three-dimensional case”, Dokl. RAN. Math. Inf. Proc. Upr., 493 (2020), 5–8; Dokl. Math., 102:1 (2020), 265–268
A. S. Adkhamova, A. L. Skubachevskii, “Damping problem for a neutral control system with delay”, Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020), 81–84; Dokl. Math., 101:1 (2020), 68–70
V. V. Liiko, A. L. Skubachevskii, “Mixed Problems for Strongly Elliptic Differential-Difference Equations in a Cylinder”, Mat. Zametki, 107:5 (2020), 693–716; Math. Notes, 107:5 (2020), 770–790
V. V. Liiko, A. L. Skubachevskii, “Strongly elliptic differential-difference equations with mixed boundary conditions in a cylindric domain”, CMFD, 65:4 (2019), 635–654
A. L. Skubachevskiĭ, “On a class of functional-differential operators satisfying the Kato conjecture”, Algebra i Analiz, 30:2 (2018), 249–273; St. Petersburg Math. J., 30:2 (2019), 329–346
A. L. Skubachevskii, “The Kato Conjecture for Elliptic Differential-Difference Operators with Degeneration in a Cylinder”, Dokl. Akad. Nauk, 478:2 (2018), 145–147; Dokl. Math., 97:1 (2018), 32–34
16.
A. L. Skubachevskii, “On a property of regularly accretive differential-difference operators with degeneracy”, Uspekhi Mat. Nauk, 73:2(440) (2018), 189–190; Russian Math. Surveys, 73:2 (2018), 372–374
Yu. O. Belyaeva, A. L. Skubachevskii, “Unique solvability of the first mixed problem for the Vlasov–Poisson system in an infinite cylinder”, Zap. Nauchn. Sem. POMI, 477 (2018), 12–34
A. L. Skubachevskii, Y. Tsuzuki, “Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 536–552; Comput. Math. Math. Phys., 57:3 (2017), 541–557
A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Uspekhi Mat. Nauk, 71:5(431) (2016), 3–112; Russian Math. Surveys, 71:5 (2016), 801–906
A. L. Skubachevskii, “Nonlocal Problems for the Vlasov–Poisson Equations in an Infinite Cylinder”, Funktsional. Anal. i Prilozhen., 49:3 (2015), 91–96; Funct. Anal. Appl., 49:3 (2015), 234–238
A. L. Skubachevskii, “Vlasov–Poisson equations for a two-component plasma in a homogeneous magnetic field”, Uspekhi Mat. Nauk, 69:2(416) (2014), 107–148; Russian Math. Surveys, 69:2 (2014), 291–330
D. A. Neverova, A. L. Skubachevskii, “Classical solutions of boundary value problems for differential-difference equations”, Differ. Uravn., 49:3 (2013), 300–309; Differ. Equ., 49:3 (2013), 288–297
D. A. Neverova, A. L. Skubachevskii, “On the Classical and Generalized Solutions of Boundary-Value Problems for Difference-Differential Equations with Variable Coefficients”, Mat. Zametki, 94:5 (2013), 702–719; Math. Notes, 94:5 (2013), 653–667
A. L. Skubachevskii, “Initial-boundary value problems for the Vlasov–Poisson equations in a half-space”, Trudy Mat. Inst. Steklova, 283 (2013), 204–232; Proc. Steklov Inst. Math., 283 (2013), 197–225
V. A. Popov, A. L. Skubachevskii, “Smoothness of generalized solutions of elliptic differential-difference equations with degenerations”, CMFD, 39 (2011), 130–140; Journal of Mathematical Sciences, 190:1 (2013), 135–146
V. A. Popov, A. L. Skubachevskii, “Smoothness of generalized solutions of elliptic difference-differential equations with degeneration near boundaries of subdomains”, Uspekhi Mat. Nauk, 66:6(402) (2011), 195–196; Russian Math. Surveys, 66:6 (2011), 1204–1206
K. A. Darovskaya, A. L. Skubachevsky, “A spectral problem with integral conditions”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011), 147–160; J. Math. Sci. (N. Y.), 179:3 (2011), 437–445
V. A. Popov, A. L. Skubachevskii, “A priori estimates for elliptic differential-difference operators with degeneration”, CMFD, 36 (2010), 125–142; Journal of Mathematical Sciences, 171:1 (2010), 130–148
A. L. Skubachevskii, “Asymptotic formulas for solutions of nonlocal elliptic problems”, Trudy Mat. Inst. Steklova, 269 (2010), 225–241; Proc. Steklov Inst. Math., 269 (2010), 218–234
A. L. Skubachevskii, “On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems”, Trudy Mat. Inst. Steklova, 260 (2008), 248–263; Proc. Steklov Inst. Math., 260 (2008), 238–253
A. M. Selitskii, A. L. Skubachevskii, “Second boundary-value problem for parabolic differential-difference equations”, Uspekhi Mat. Nauk, 62:1(373) (2007), 207–208; Russian Math. Surveys, 62:1 (2007), 191–192
N. B. Zhuravlev, A. L. Skubachevskii, “Hyperbolicity of Periodic Solutions of Functional Differential Equations with Several Delays”, Trudy Mat. Inst. Steklova, 256 (2007), 148–171; Proc. Steklov Inst. Math., 256 (2007), 136–159
A. M. Selitskii, A. L. Skubachevskii, “The second boundary-value problem for parabolic differential-difference equations”, Tr. Semim. im. I. G. Petrovskogo, 26 (2007), 324–347; J. Math. Sci. (N. Y.), 143:4 (2007), 3386–3400
H. Walther, A. L. Skubachevskii, “On the Hyperbolicity of Rapidly Oscillating Periodic Solutions of Functional Differential Equations”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 82–85; Funct. Anal. Appl., 39:1 (2005), 68–70
O. A. Kovaleva, A. L. Skubachevskii, “Solvability of nonlocal elliptic problems in weight spaces”, Mat. Zametki, 67:6 (2000), 882–898; Math. Notes, 67:6 (2000), 743–757
V. V. Pod'yapol'skii, A. L. Skubachevskii, “Spectral asymptotics of strongly elliptic differential-difference operators”, Differ. Uravn., 35:6 (1999), 793–800; Differ. Equ., 35:6 (1999), 794–802
L. E. Rossovskii, A. L. Skubachevskii, “Solvability and regularity of solutions of some classes of elliptic functional-differential equations”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 66 (1999), 114–192; J. Math. Sci. (New York), 104:2 (2001), 1008–1059
A. L. Skubachevskii, R. V. Shamin, “First mixed problem for a parabolic difference-differential equation”, Mat. Zametki, 66:1 (1999), 145–153; Math. Notes, 66:1 (1999), 113–119
A. L. Skubachevskii, “On the Hopf bifurcation for a quasilinear parabolic functional-differential equation”, Differ. Uravn., 34:10 (1998), 1394–1401; Differ. Equ., 34:10 (1998), 1395–1402
E. I. Galakhov, A. L. Skubachevskii, “On non-negative contractive semigroups with non-local conditions”, Mat. Sb., 189:1 (1998), 45–78; Sb. Math., 189:1 (1998), 43–74
A. L. Skubachevskii, “On Normality of Some Elliptic Functional Differential Operators”, Funktsional. Anal. i Prilozhen., 31:4 (1997), 60–65; Funct. Anal. Appl., 31:4 (1997), 273–277
V. V. Pod'yapol'skii, A. L. Skubachevskii, “On the completeness and basis property for a system of root functions of strongly elliptic functional-differential operators”, Uspekhi Mat. Nauk, 51:6(312) (1996), 219–220; Russian Math. Surveys, 51:6 (1996), 1220–1222
A. L. Skubachevskii, “On some properties of elliptic and parabolic functional-differential equations”, Uspekhi Mat. Nauk, 51:1(307) (1996), 169–170; Russian Math. Surveys, 51:1 (1996), 169–170
K. Cook, L. E. Rossovskii, A. L. Skubachevskii, “A boundary value problem for a functional-differential equation with a linearly transformed argument”, Differ. Uravn., 31:8 (1995), 1348–1352; Differ. Equ., 31:8 (1995), 1294–1299
A. L. Skubachevskii, “On the problem of damping a control system with aftereffect”, Dokl. Akad. Nauk, 335:2 (1994), 157–160; Dokl. Math., 49:2 (1994), 282–286
A. L. Skubachevskii, “Generalized and classical solutions of boundary value problems for
differential-difference equations”, Dokl. Akad. Nauk, 334:4 (1994), 433–436; Dokl. Math., 49:1 (1994), 132–137
A. L. Skubachevskii, “Boundary value problems for differential-difference equations with
incommensurable shifts”, Dokl. Akad. Nauk, 324:6 (1992), 1155–1158; Dokl. Math., 45:3 (1992), 695–699
A. L. Skubachevskii, G. M. Steblov, “On the spectrum of differential operators with a domain that is
not dense in $L_2(0,1)$”, Dokl. Akad. Nauk SSSR, 321:6 (1991), 1158–1163; Dokl. Math., 44:3 (1992), 870–875
A. L. Skubachevskii, “The method of cut-off functions in the theory of nonlocal problems”, Differ. Uravn., 27:1 (1991), 128–139; Differ. Equ., 27:1 (1991), 103–112
A. L. Skubachevskii, E. L. Tsvetkov, “The second boundary value problem for elliptic differential-difference equations”, Differ. Uravn., 25:10 (1989), 1766–1776; Differ. Equ., 25:10 (1989), 1245–1254
A. L. Skubachevskii, “Eigenvalues and eigenfunctions of some nonlocal boundary value problems”, Differ. Uravn., 25:1 (1989), 127–136; Differ. Equ., 25:1 (1989), 101–108
A. L. Skubachevskii, “Solvability of elliptic problems with nonlocal boundary conditions”, Dokl. Akad. Nauk SSSR, 291:3 (1986), 551–555
59.
A. L. Skubachevskii, “Elliptic problems with nonlocal conditions near the boundary”, Mat. Sb. (N.S.), 129(171):2 (1986), 279–302; Math. USSR-Sb., 57:1 (1987), 293–316
A. L. Skubachevskii, “Smoothness of generalized solutions of the first boundary-value problem for an elliptic difference-differential equation”, Mat. Zametki, 34:1 (1983), 105–112; Math. Notes, 34:1 (1983), 537–541
A. L. Skubachevskii, “Nonlocal elliptic problems with a parameter”, Mat. Sb. (N.S.), 121(163):2(6) (1983), 201–210; Math. USSR-Sb., 49:1 (1984), 197–206
A. L. Skubachevskii, “On the spectrum of some nonlocal elliptic boundary value problems”, Mat. Sb. (N.S.), 117(159):4 (1982), 548–558; Math. USSR-Sb., 45:4 (1983), 543–553
G. A. Kamenskii, A. D. Myshkis, A. L. Skubachevskii, “On the minimum of a quadratic functional and on linear boundary value problems of elliptic type with deviating arguments”, Differ. Uravn., 16:8 (1980), 1469–1473
G. A. Kamenskii, A. D. Myshkis, A. L. Skubachevskii, “The minimum of a quadratic functional, and linear elliptic boundary-value problems with deviating arguments”, Uspekhi Mat. Nauk, 34:3(207) (1979), 197–198; Russian Math. Surveys, 34:3 (1979), 201–202
A. L. Skubachevskii, “A certain property of the solutions of a second order linear differential equation of unstable type with retarded argument”, Differ. Uravn., 11:4 (1975), 760–761
71.
A. L. Skubachevskii, “The oscillatory solutions of a second order linear homogeneous differential equation with retarded argument”, Differ. Uravn., 11:3 (1975), 462–469
2024
72.
A. Ya. Belov, V. M. Buchstaber, V. B. Vasilyev, Yu. P. Virchenko, S. K. Kuizheva, A. G. Kusraev, D. K. Mamyi, A. B. Muravnik, A. V. Pskhu, S. A. Rozanova, Z. A. Saidov, A. L. Semenov, S. M. Sitnik, A. L. Skubachevskii, A. P. Soldatov, E. L. Shishkina, A. G. Yagola, “Sultan Nazhmudinovich Askhabov (on the 70-th anniversary of his birth)”, Chebyshevskii Sb., 25:2 (2024), 5–19
2021
73.
A. I. Aptekarev, D. E. Apushkinskaya, O. V. Besov, V. I. Burenkov, V. V. Vlasov, R. V. Gamkrelidze, M. L. Gol'dman, G. V. Demidenko, V. G. Zadorozhniy, V. V. Kozlov, G. G. Lazareva, S. P. Novikov, V. M. Savchin, V. A. Sadovnichii, A. L. Skubachevskii, A. P. Soldatov, D. V. Treschev, M. A. Ragusa, H.-O. Walther, “Vladimir Mikhailovich Filippov”, CMFD, 67:3 (2021), 423–426
O. V. Anashkin, E. M. Varfolomeev, V. I. Voytitsky, V. I. Donskoy, D. A. Zakora, A. B. Muravnik, M. A. Muratov, Yu. S. Pashkova, V. È. Petrov, E. V. Plokhaya, A. L. Skubachevskii, P. A. Starkov, T. A. Suslina, D. O. Tsvetkov, V. N. Chekhov, A. A. Shkalikov, A. I. Yakovlev, “Nikolay Dmitrievich Kopachevsky. March 25, 1940 — May 18, 2020”, CMFD, 66:2 (2020), 157–159
2017
75.
A. A. Amosov, Yu. A. Dubinskii, V. V. Kozlov, M. K. Kerimov, L. G. Popov, A. L. Skubachevskii, V. M. Filippov, M. F. Cherepova, “In memory of Professor Stanislav Ivanovich Pokhozhaev, Corresponding Member of RAS”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 379–380
2011
76.
M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010”, CMFD, 39 (2011), 5–10; Journal of Mathematical Sciences, 190:1 (2013), 1–7
2006
77.
A. L. Skubachevskii, “The Fourth International Conference on Differential and Functional-Differential Equations”, Uspekhi Mat. Nauk, 61:4(370) (2006), 201–202; Russian Math. Surveys, 61:4 (2006), 791–792
О гладкости собственных функций дифференциально–разностного оператора второго порядка A. L. Skubachevskii, R. Yu. Vorotnikov VI International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev November 15, 2023 15:20
Гипотеза Като о квадратном корне из оператора A. L. Skubachevskii Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics November 28, 2018 16:00
Об одном классе операторов, удовлетворяющих гипотезе Като A. L. Skubachevskii Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) August 15, 2018 14:00
Уравнения Власова в бесконечном цилиндре A. L. Skubachevskii Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics October 16, 2013 16:00
Opening ceremony D. V. Anosov, A. G. Sergeev, A. L. Skubachevskii Sixth International Conference on Differential and Functional Differential Equations DFDE-2011 August 15, 2011 11:00
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