01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
12.11.1941
E-mail:
Keywords:
integral and integral-differencial equations; functional analysis (factorization of operators etc.); mathematical physics (radiative transfer, kinetic theory of gases etc.); stochastic processes; multidimensional complex analysis; astrophysics.
Subject:
The theory of nonlinear factorization equations (NFE) of integral and other linear operators was founded, including various applications. Generalized Volterian factorization problem for non-invertible integral operators was formulated and solved. A complete theory of Wiener–Hopf scalar and vector integral equations for conservative and supercritical (singular) cases was developed, using NFE. A theory of generalized Ambartsumian equation and Riccati-type operator equation was developed. A principal new approach to the solution of convolution-type integral equations on a finite interval was developed, including applications in radiative transfer (RT) theory. A structural theory for renewal equations (on the half-line and on the whole line) and Markov renewal equations was developed, including new-type limit and asymptotic theorems. For the first time the theory and solution methods for RT problems in spectral lines in general laws of non-coherent scattering, as well as - the mathematical theory of anisotrope scattering with summable indicatrix (including solution of Miln problem) was developed. The method of self-consisting optical depths (coming from Edington and V. Ambartsumian ideas) for exact solution of non-linear RT problems, was developed. Some factorization and other, methods to efficient numerical-analytical solution of RT problems and problems of kinetic theory of gases, was developed. The domains of normal convergence of multidimensional Loran series was constructed.
Biography
Graduated from Faculty of Mathematics and Mechanics of Yerevan State University in 1963 (department of math. analysis and theory of functions). Was Lenin scholarship holder. Ph. D. thesis was defended in 1968. D. Sci. thesis was defended in 1979. A list of my works contains more than 130nbsp;titles. Since 1971 I have led the research seminar on integral equations and mathematical physics; 35 years of teaching experience at Yerevan State University and other high schools; was head of some math. chairs; supervision of 16 Ph. D. and 5 D. Sci. thesis.
Member of a number local and international Scientific Boards.
Main publications:
Engibaryan N. B., “Uravneniya v svertkakh, soderzhaschie singulyarnye veroyatnostnye raspredeleniya”, Izv. RAN, ser. matem., 60:2 (1996), 21–48
N. B. Engibaryan, “On the combination of Lebesgue and Riemann integrals in theory of convolution equations”, TMF, 218:1 (2024), 80–87; Theoret. and Math. Phys., 218:1 (2024), 68–74
2018
2.
N. B. Engibaryan, “On the factorization of matrix and operator Wiener–Hopf integral equations”, Izv. RAN. Ser. Mat., 82:2 (2018), 33–42; Izv. Math., 82:2 (2018), 273–282
2015
3.
N. B. Engibaryan, “A discrete model for nonlinear problems of Radiation Transfer: principle of invariance and factorization”, Matem. Mod., 27:5 (2015), 127–136
A. G. Barseghyan, N. B. Engibaryan, “Approximate solution of Wiener–Hopf integral equations and its discrete counterparts”, Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015), 836–845; Comput. Math. Math. Phys., 55:5 (2015), 834–843
N. B. Engibaryan, A. G. Barseghyan, “Transport equations”, TMF, 180:2 (2014), 206–216; Theoret. and Math. Phys., 180:2 (2014), 932–941
6.
N. B. Engibaryan, A. Kh. Khachatryan, “Solvability of an integrodifferential equation arising in the nonlocal interaction of waves”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 834–844; Comput. Math. Math. Phys., 54:5 (2014), 834–844
N. B. Engibaryan, “Differential equations where the derivative is taken with respect to a measure”, Mat. Sb., 202:2 (2011), 93–106; Sb. Math., 202:2 (2011), 243–256
2010
8.
N. B. Engibaryan, A. Barseghyan, “Random walks and mixtures of Gamma-distributions”, Teor. Veroyatnost. i Primenen., 55:3 (2010), 571–577; Theory Probab. Appl., 55:3 (2011), 528–535
N. B. Engibaryan, “On the factorization of integral operators on spaces of summable functions”, Izv. RAN. Ser. Mat., 73:5 (2009), 67–82; Izv. Math., 73:5 (2009), 921–937
N. B. Engibaryan, A. Kh. Khachatryan, “Integro-differential equation of non-local wave interaction”, Mat. Sb., 198:6 (2007), 89–106; Sb. Math., 198:6 (2007), 839–855
N. B. Engibaryan, “On the fixed points of monotonic operators in the critical case”, Izv. RAN. Ser. Mat., 70:5 (2006), 79–96; Izv. Math., 70:5 (2006), 931–947
N. B. Engibaryan, “A renewal equation in a multidimensional space”, Teor. Veroyatnost. i Primenen., 49:4 (2004), 779–785; Theory Probab. Appl., 49:4 (2005), 737–744
2003
14.
N. B. Engibaryan, “Asymptotic and structural theorems for the Markov renewal equation”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 62–77; Theory Probab. Appl., 48:1 (2004), 80–92
2002
15.
N. B. Engibaryan, “Conservative systems of integral convolution equations
on the half-line and the entire line”, Mat. Sb., 193:6 (2002), 61–82; Sb. Math., 193:6 (2002), 847–867
N. B. Engibaryan, “Setting and solving several factorization problems for integral operators”, Mat. Sb., 191:12 (2000), 61–76; Sb. Math., 191:12 (2000), 1809–1825
N. B. Engibaryan, A. Kh. Khachatryan, “Exact linearization of the sliding problem for a dilute gas in the Bhatnagar–Gross–Krook model”, TMF, 125:2 (2000), 339–342; Theoret. and Math. Phys., 125:2 (2000), 1589–1592
N. B. Engibaryan, “Radiative transfer in a spherically symmetric medium”, Zh. Vychisl. Mat. Mat. Fiz., 39:10 (1999), 1730–1739; Comput. Math. Math. Phys., 39:10 (1999), 1660–1669
N. B. Engibaryan, B. N. Enginbarian, “Convolution equation with a completely monotonic kernel on the half-line”, Mat. Sb., 187:10 (1996), 53–72; Sb. Math., 187:10 (1996), 1465–1485
N. B. Engibaryan, L. G. Arabadzhyan, “Some factorization problems for integral operators of convolution type”, Differ. Uravn., 26:8 (1990), 1442–1452; Differ. Equ., 26:8 (1990), 1069–1078
R. S. Vardanyan, N. B. Engibaryan, “The solution of one class of convolution-type integral equations”, Zh. Vychisl. Mat. Mat. Fiz., 29:9 (1989), 1291–1300; U.S.S.R. Comput. Math. Math. Phys., 29:5 (1989), 20–27
L. G. Arabadzhyan, N. B. Engibaryan, “Convolution equations and nonlinear functional equations”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 22 (1984), 175–244; J. Soviet Math., 36:6 (1987), 745–791
N. B. Engibaryan, L. G. Arabadzhyan, “Systems of Wiener–Hopf integral equations, and nonlinear factorization equations”, Mat. Sb. (N.S.), 124(166):2(6) (1984), 189–216; Math. USSR-Sb., 52:1 (1985), 181–208
N. B. Engibaryan, M. A. Mnatsakanyan, “Linear algebraic systems with Toeplitz matrices”, Zh. Vychisl. Mat. Mat. Fiz., 17:5 (1977), 1102–1116; U.S.S.R. Comput. Math. Math. Phys., 17:5 (1977), 3–17
N. B. Engibaryan, M. A. Mnatsakanyan, “An integral equation with a difference kernel”, Mat. Zametki, 19:6 (1976), 927–932; Math. Notes, 19:6 (1976), 541–544
N. B. Engibaryan, A. A. Arutyunyan, “Integral equations on the half-line with difference kernels and nonlinear functional equatons”, Mat. Sb. (N.S.), 97(139):1(5) (1975), 35–58; Math. USSR-Sb., 26:1 (1975), 31–54
Методы решения уравнений свертки N. B. Engibaryan Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS February 27, 2014 11:00
5.
Об уравнениях переноса N. B. Engibaryan Conference "Mathematical Physics. Vladimirov-90" dedicated to the 90th anniversary of academician V. S. Vladimirov November 13, 2013 13:00
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