# Khachatur Khachatryan

Khachatur Khachatryan (Armenian: Խաչատուր Աղավարդի Խաչատրյան), (1 July 1982, Armenia) is an Armenian scientist and mathematician.

## Early life and education

Khachatur Khachatryan was born on July 1, 1982, in Yerevan, Armenia.
In 1998 graduated from Phys. math. school No. 1 named after A. Shahinyan with honors. He graduated from the Faculty of Mathematics of Yerevan State University in 2004 with honors (Department of Differential Equations and Functional Analysis).
In 2004, he entered graduate school (aspirant) at Yerevan State University. In 2006, in the specialized council 050 of Yerevan State University, he defended his PhD thesis on the topic “On factorization methods for solving a certain class of integral and integro-differential equations on the semi-axis.” (specialty 01.01.02 - “Differential equations”), scientific supervisor, Doctor of Phys-Math. sciences, prof. N. B. Yengibaryan, official opponents: Doctor of Phys-Math. sciences, prof. Sergeev, Armen Glebovich, candidate of Phys-Math. sciences, Associate Professor A. G. Kamalyan, Leading organization: Armenian State Pedagogical University.
In 2011, in the specialized council 050 of Yerevan State University, he defended his doctoral dissertation (= habilitation) on the topic “Questions of the solvability of some nonlinear integral and integro-differential equations with non-compact operators in the critical case” (specialty 01.01.02 - “Differential equations”), official opponents: Doctor of Phys-Math. sciences, prof. Zabreiko, Pyotr Petrovich, Doctor of Phys-Math. sciences, prof. A. S. Krivosheev, Academician of the National Academy of Sciences of Armenia, Doctor of Phys-Math. sciences, prof. A. B. Nersesyan, Leading organization: Steklov Mathematical Institute of the Russian Academy of Sciences.

## Career

Since 2018 Khachatryan is a full professor of Mathematics, and the scientific supervisor of seven candidate dissertations (PhD theses).
He teaches courses in functional analysis, differential equations, equations of mathematical physics, calculus of variations, mathematical analysis, nonlinear operator equations, convolution type equations.
Since 2005, he has been working in the Department of Methods of Mathematical Physics of the Institute of Mathematics of the National Academy of Sciences of Armenia. From 2004 to 2006 and since 2012 he teaches at Yerevan State University (YSU). In 2015-2017 taught at the Yerevan branch of Moscow State University. M. V. Lomonosov (part-time). Since 2019 he has been teaching at the Russian-Armenian Slavic University. Since 2019, the main executor of the Russian Science Foundation grant (project No. 19-11-00223) Moscow State University . From 2020 Head of the Department of Differential Equations, and from 2021, Head of the Department of Theory of Functions and Differential Equations, Yerevan State University.

## Scientific interests

* Differential equations
* Equations of mathematical physics
* Nonlinear analysis
* Integral and integro-differential equations with Hammerstein and Urysohn type operators
* Integral equations of convolution type
* Factorization of integral and integro-differential operators
* Boltzmann equation
* p-adic string theory
* Nonlinear pseudodifferential equations
* Mathematical modeling of the geographic spread of the epidemic
* Nonlinear parabolic equations

## State awards and honorary titles

* 2014 Winner of the "Efficient Researcher" competition (Natural Sciences) (Top 100)
* 2013 1st-class prize of the RA NAS "Best scientific work of 2013" competition,
* 2013 Winner of the first prize after Sergey Mergelyan for young scientists (Mathematics and Informatics)
* 2021 Winner of the "Efficient Researcher" competition (Natural Sciences) (Top 100)
* 2020 Winner of the "Efficient Researcher" competition (Natural Sciences) (Top 100)
* 2018 Winner of the "Efficient Researcher" competition (Natural Sciences) (Top 100)
* 2016 Winner of the "Efficient Researcher" competition (Natural Sciences) (Top 100)
* 2019 Prize of the President of the Republic of Armenia

## Memberships

* Deputy Chairman of Yerevan State University 050 Professional Council
* Member of the editorial board of the Journal of Contemporary Mathematical Analysis
* Member of Professional Council 058 of Yerevan State University
* Member of the Scientific Council of the Institute of Mathematics of the National Academy of Sciences of the Republic of Armenia
* Member of the Scientific Council of the Faculty of Mathematics and Mechanics of Yerevan State University
* Member of the Scientific Council of the Institute of Mathematics and Informatics of the Armenian-Russian University
* Member of the Union of Mathematicians of Armenia

## Publications

He has more than 150 scientific articles in various scientific international journals.
* Kh.A. Khachatryan, H.S. Petrosyan, “On a class of nonlinear integral equations of the Hammerstein–Volterra type on a semiaxis”, Russian Math. (Iz. VUZ), 67:1 (2023), 64–73
* H.S. Petrosyan, Kh.A. Khachatryan, “Uniqueness of the Solution of a Class of Integral Equations with Sum-Difference. Kernel and with Convex Nonlinearity on the Positive Half-Line”, Math. Notes, 113:4 (2023), 512–524
* Kh.A. Khachatryan, H.S. Petrosyan, “On the nontrivial solvability of a system nonlinear integral equations on the whole line”, Izv. RAN. Ser. Mat., 87:5 (2023), 215–231
* A.Kh. Khachatryan, Kh.A. Khachatryan, H.S. Petrosyan, “On nonlinear convolution-type integral equations in the theory of p-adic strings”, Theoret. and Math. Phys., 216:1 (2023), 1068–1081
* Kh.A. Khachatryan, H.S. Petrosyan, S.M. Andriyan, “On the solubility of a class of two-dimensional integral equations on a quarter plane with monotone nonlinearity”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, 2, 19–38
* Kh.A. Khachatryan, H.S. Petrosyan, “On summable solutions of a class of nonlinear integral equations on the whole line”, Izv. Math., 86:5 (2022), 980–991
* A.Kh. Khachatryan, Kh.A. Khachatryan, A.Zh. Narimanyan, “Existence and uniqueness result for reaction-diffusion model of diffusive population dynamics”, Тр. ММО, 83:2 (2022), 219–239
* Kh.A. Khachatryan, H.S. Petrosyan, “On a class of nonlinear integro-differential equations”, Mat. Tr., 25:1 (2022), 192–220
* A.G. Sergeev, A.Kh. Khachatryan, Kh.A. Khachatryan, “Математическая модель распространения пандемии типа COVID-19”, Tr. Mosk. Mat. Obs., 83, no. 1, MCCME, M., 2022, 63–75
* A.Kh. Khachatryan, Kh.A. Khachatryan, H.S. Petrosyan, “Solvability of Two-Dimensional Integral Equations with Monotone Nonlinearity”, Journal of Mathematical Sciences, New York, 257:3, (2021), 720-731
* A.Kh. Khachatryan, Kh.A. Khachatryan, H.S. Petrosyan, “On Positive Bounded Solutions of One Class of Nonlinear Integral Equations with the Hammerstein–Nemytskii Operator”, Differential Equations, vol. 57, iss. 6, (2021) 768–779
* A. Kh. Khachatryan, Kh. A. Khachatryan, “On solvability of one infinite system of nonlinear functional equations in the theory of epidemics”, Eurasian Math. J., 11:2 (2020), 52–64
* Kh.A.Khachatryan, A.Zh.Narimanyan, A.Kh.Khachatryan, “On Mathematical Modelling of Temporial Spatial Spread of Epidemics” (France), Mathematical Modelling of Natural Phenomena, 15:6 (2020), 1-14
* Kh.A. Khachatryan, H.S. Petrosyan. Solvability of a Nonlinear Problem in Open-Closed p-Adic String Theory. Differential Equations 56, 1371–1378 (2020)
* Kh. A. Khachatryan, “Solvability of some nonlinear boundary value problems for singular integral equations of convolution type”, Trans. Moscow Math. Soc., 81:1 (2020), 1–31
* A. G. Sergeev, Kh. A. Khachatryan, “On the solvability of a class of nonlinear integral equations in the problem of a spread of an epidemic”, Trans. Moscow Math. Soc., 80 (2019), 95–11
* Kh. A. Khachatryan, “On the solubility of certain classes of non-linear integral equations in p-adic string theory”, Izv. Math., 82:2 (2018), 407–427
* Kh. A. Khachatryan, H. S. Petrosyan, “One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity”, Russian Math. (Iz. VUZ), 62:6 (2018), 43–55
* A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear integral equation in dynamical string theory”, Theoret. and Math. Phys., 195:1 (2018), 529–537
* A.Kh.Khachatryan, Kh. A. Khachatryan, “Solvability of a class of nonlinear pseudo-differential equations in R n”, p-adic Numbers, Ultrametric Analysis and Applications, 10:2 (2018), 90-99
* A. Kh. Khachatryan, Kh. A. Khachatryan, “A one-parameter family of positive solutions of the non-linear stationary Boltzmann equation (in the framework of a modified model)”, Russian Math. Surveys, 72:3 (2017), 571–573
* Kh.A.Khachatryan, “On solvability of one class nonlinear integral equations on whole line with a weak singularity at zero”, p-Adic Numbers, Ultrametric Analysis and Applications, 9:4 (2017), 292-305
* A. Kh. Khachatryan, Kh. A. Khachatryan, “Some problems concerning the solvability of the nonlinear stationary Boltzmann equation in the framework of the BGK model”, Trans. Moscow Math. Soc., 77 (2016), 87–106
* A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear model Boltzmann equation in the problem of a plane shock wave”, Theoret. and Math. Phys., 189:2 (2016), 1609–1623
* Kh. A. Khachatryan, “Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line”, Izv, Math., 79:2 (2015), 411-430.
* K. A. Khachatryan, Ts. E. Terdzhyan, “On the solvability of one class of nonlinear integral equations in L1(0,+∞)L1(0,+∞)”, Siberian Adv. Math., 25:4 (2015), 268–275
* A.Kh.Khachatryan, Kh.A.Khachatryan, Ts. E. Terdjyan, “On solvability of one integral equation on half line with Chebyshev polynomial nonlinearity”, P-Adic Numbers, Ultrametric Analysis, and Applications, 7:3 (2015), 228-237
* A.Kh.Khachatryan, Kh.A.Khachatryan, T.H. Sardaryan, “On One Nonlinear Boundary-Value Problem in Kinetic Theory of Gases”, Journal of Mathematical Physics, Analysis, Geometry, 10:3 (2014), 320-327
* A.Kh. Khachatryan, Kh. A. Khachatryan, “Qualitative difference between solutions of stationary model Boltzmann equations in the linear and nonlinear cases”, Theoret. and Math. Phys., 180:2 (2014), 990–1004
* Khachatur A. Khachatryan and Mikael G. Kostanyan, “On the solvability of a nonlinear second-order integro-differential equation with sum-difference kernel on a semiaxis”, Journal of Mathematical Sciences, 181:1 (2012), 65-77
* Aghavard Kh.Khachatryan, Khachatur A.Khachatryan, “Hammerstein -Nemitski type Nonlinear integral equations on half-line in space L1(R+) and Linfinity(R+)”, Acta Univ. Palacki. Olomuc., Fac.rer. nat., Mathematica, 52:1 (2013), 89-100
* Kh. A. Khachatryan, “On a class of integral equations of Urysohn type with strong non-linearity”, Izv. Math., 76:1 (2012), 163–189
* Kh. A. Khachatryan, “On solvability one Hammerstein–Nemitski type nonlinear integral differential equation with noncompact operator in W11(R+)W11(R+)”, St. Petersburg Math. J., 24:1 (2013), 167–183
* A.Kh.Khachatryan, Kh.A.Khachatryan, “Qualitative difference between solutions for a model Boltzmann equation in the linear and nonlinear cases”, Theoretical and Mathematical Physics, 172:3 (2012), 1315-1320; A. Kh. Khachatryan, Kh. A. Khachatryan, “Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases”, Theoret. and Math. Phys., 172:3 (2012), 1315–1320
* A. Kh. Khachatryan, Kh. A. Khachatryan, “Existence and Uniqueness Theorem For a Hammerstein Nonlinear Integral Equation”, Opuscula Mathematica (POLAND), 31:3 (2011), 393–398
* Kh. A. Khachatryan, “On a Class of Nonlinear Integral Equations With a Noncompact Operator”, Journal of Contemporary Mathematical Analysis, 46:2 (2011), 89–100
* A. Khachatryan, Kh. Khachatryan, “On solvability of a nonlinear problem in theory of income distribution”, Eurasian Math. J., 2:2 (2011), 75–88
* A. Kh. Khachatryan, Kh. A. Khachatryan, “A nonlinear integral equation of Hammerstein type with a noncompact operator”, Sb. Math., 201:4 (2010), 595–606
* Kh. A. Khachatryan, “Solubility of a class of second-order integro-differential equations with monotone non-linearity on a semi-axis”, Izv. Math., 74:5 (2010), 1069–1082
* A. Kh. Khachatryan and Kh. A. Khachatryan, “On an Integral Equation With Monotonic Nonlinearity”, Memoirs on Differential Equations and Mathematical Physics, 51:3 (2010), 59–72