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Khachatryan, Khachatur Aghavardovich

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Total publications: 48
Scientific articles: 48
Presentations: 8

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Khachatryan, Khachatur Aghavardovich
Professor
Doctor of physico-mathematical sciences (2011)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 1.07.1982
Phone: +374(10) 27 43 49, +374 (10) 56 72 64, +374 (91) 300 251 (моб.)
Fax: +374 (10) 58 15 97
E-mail: ,
Keywords: Sobolev space, Carathéodory condition, Wiener–Hopf operator.
UDC: 517.968, 517.958, 517.968.4, 517.968.48, 517.968.74, 517.968.43, 517.988.63, 517.968.22, 512.625.5
MSC: 45Gxx, 35XX, 35G55, 35G50, 45G05, 45M20, 65R20,35G55, 35G50, 35Q20, 82B40, 45J05, 45G10, 65R20, 60E05, 76P05

Subject:

Hammerstein and Urysohn types nonlinear integral and integro-differential equations.

Biography

Education and scientific degree:

• 1998 № 1, Phys-Math. school at Yerevan State University (certificate with honours)

• 2004 Yerevan State University, Mathematical department (diploma with honours)

• 2004–2006 Aspirantura, the Yerevan State University (Scientific adviser – Prof. N.B. Yengibaryan)

• 2006 Candidate of Scienece (=PhD) in Physics and Mathematics

Dissertation: “On factorization methods for solution of some classes of integral and integro-differential equations on half line”, (A.01.02, Differential Equations), Yerevan State University.

• 2011 Doctor of Science in Physics and Mathematics ( =Habilitation)

Dissertation: “Questions of solvability of some nonlinear integral and integro-differential equations with noncompact operators in critical case”, (A.01.02, Differential Equations), Yerevan State University.

Academic appointments:

2005–present Department of Methods of Mathematical Physics, Institute of Mathematics NAS, Armenia

2016–present Head Scientist researcher in Department of Methods of Mathematical Physics, Institute of Mathematics NAS, Armenia ,

2018-- professor,

Teaching:

2004–2006, 2012–present

General courses Mathematical Analysis, Differential Equations, Mathematical Physics, Calculus of Variations, Optimal Control,

Special courses

Positive Solutions of Operator Equations, Convolution type Integral Equations, Nonlinear Analysis,

at the Departments of Mathematics and Mechanics, Computational Mathematics and Informatics of Yerevan State University.

Publication:

69 papers and 25 theses.

Conferences, International collaboration:

• 2002 ISAAC conference on Complex analysis Differential equations and Related topics. Yerevan, Armenia

• 2004 International Workshop Global and Geometric aspects of nonlinear PDF. Yerevan, Armenia

• 2005 International Conference Harmonic Analysis and Approxinations. Tsaghkadzor, Armenia

• 2006 Russian-Armenia Workshop Mathematical physics and Related topics. Yerevan, Armenia

• 2008 Second russian-Armenian Workshop Mathematical physics, complex analisis and Related topics, Moscow, Russia

• 2008 International conference Multivariate statistical analysis and Econometrics. Moscow, Russia

• 2009 Inernational conference p-adic mathematical physics Hrodno (Belarus)

• 2010 Third russian-Armenian Workshop on Mathematical physics, complex analysis, and related topics. Tsaghkadzor, Armenia

• 2012 Third International Conference on Mathematical Physics and Its Applications (Russia, Samara), Steklov Mathematical Institute of the Russian Academy of Sciences, Samara State Technical University,Samara State University.

• 2012 4th Russian-Armenian workshop on mathematical physics, complex analysis and related topics, Krasnoyarsk, Russia, Siberian Federal University, Steklov Mathematical Institute of Russian Academy of Sciences, Institute of Mathematics of National Academy of Sciences of Republic of Armenia.

• 2013 International Conference "Mathematical Physics. "Vladimirov-90" dedicated to the 90th anniversary of academician V. S. Vladimirov, November 13, Moscow, Steklov Mathematical Institute of RAS.

• 2014 4th International Conference on Mathematical Physics and Its Applications (Russia, Samara), Steklov Mathematical Institute of the Russian Academy of Sciences, Samara State Technical University,Samara State University.

• 2014 5th Russian-Armenian workshop on mathematical physics, complex analysis and related topics, Yerevan, Republic of Armenia, Institute of Mathematics of National Academy of Sciences of , Steklov Mathematical Institute of Russian Academy of Sciences.

• 2016 6th Russian-Armenian Workshop on Mathematical Analysis, Mathematical Physics and Analytical Mechanics" September 11–16, 2016, Rostov-na-Donu. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Southern Federal University, Rostov-on-Don. Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan Don State Technical University, Rostov-on-Don.

Scope of scientific interests:

Nonlinear Analysis, integral and integro-differential equations with Hammerstein and Urysohn type operators. Convolution type integral equations, the theory of factorization of integral and integro-differential operators. Boltzmann equation.

PhD Students:

1. Marine Broyan (2009–2013),

Dissertation: “Questions of solvability of nonlinear integral and Integro-Differential Equations with noncompact operators and their discrete analogy” (A.01.02, Differential Equations), Yerevan, SEUA, 2013, PhD,

2. Haykanush Petrosyan (2012–2015)

Dissertation: “Some integral and integro-Differential Equations with Hammerstein Type noncompact operators on semi-axis” (A.01.02, Differential Equations and Mathematical Physics), Yerevan State University, 2015, PhD,

3. Tigran Sardaryan (2013– 2016)

Dissertation: "The issues of global solvability for some nonlinear problems of physical kinetics" (A.01.02, Differential Equations and Mathematical Physics), Yerevan State University, 2016, PhD,

4. Hermine Azizyan (2013– 2016)

Dissertation: "The Issues of Solvability for some convolution type integral and integro-differential equations", (A.01.02, Differential Equations and Mathematical Physics), Yerevan State University, 2016, PhD.

5. Arpenik Kroyan (2014–present)

Awards and prizes:

• 1997 First prize in Republic mathematical olympiad between lyceums,

• 2003, 2004 Scholarship of "Research Mathematics" foundation,

• 2003 First prize of competition the "best student" of YSU,

• 2013 Laureate of the first prize after Sergey Mergelyan for young scientist (Mathematics and Informatics),

• 2013 Laureate of the first prize “Best scientific work for young scientist”, (Mathematics and Mechanics), National Academy of Sciences of Armenia,

• 2013 Winner of “Research Support Program of young Scientist-2013”, (Mathematics ), State Committee of Sciences of Armenia, Ministry of Education and Science,

• 2014 Winner of “Productive Scientist-2014”, Section on Natural Sciences (Top 100), State Committee of Sciences of Armenia, Ministry of Education and Science.

• 2016 Winner of “Productive Scientist-2016”, Section on Natural Sciences (Top 100), State Committee of Sciences of Armenia, Ministry of Education and Science.

• 2016 Winner of “Research Support Program of young Scientist-2016”, (Mathematics ), State Committee of Sciences of Armenia, Ministry of Education and Science

• 2018 Winner of “Productive Scientist-2018”, Section on Natural Sciences (Top 100), State Committee of Sciences of Armenia, Ministry of Education and Science.

2019-- 2021 The main performer of the grant of the Russian Science Foundation (project No. 19-11-00223)

Scientific-organizational responsibilities:

• Member of the Academic Council of Institute of Mathematics of National Academy Sciences Armenia

• Member of Armenian Mathematical Union

• Member of specialized Committee on Mathematics №050 at Yerevan State University.

• Member of the Editorial Board of the Journal of Contemporary Mathematical Analysis

Interview with Kh.A.Khachatryan: http://www.mediamax.am/en/news/mathart/24840

Family status:

2004 Married Marianna Bareghamyan, 2 children, 1 son (Aghavard) and 1 daughter (Anahit).


http://www.mathnet.ru/eng/person27540
http://scholar.google.com/citations?user=egljm6UAAAAJ&hl=en
http://zbmath.org/authors/?q=ai:khachatryan.khachatur-a
https://mathscinet.ams.org/mathscinet/MRAuthorID/703517
https://www.researchgate.net/profile/90d8282131

Publications in Math-Net.Ru
2019
1. A. Kh. Khachatryan, Kh. A. Khachatryan, “A uniqueness theorem for a nonlinear singular integral equation arising in $p$-adic string theory”, Proceedings of the YSU, Physical and Mathematial Scineces, 53:1 (2019),  17–22  mathnet
2018
2. Kh. A. Khachatryan, S. M. Andriyan, A. A. Sisakyan, “On the solvability of a class of boundary value problems for systems of the integral equations with power nonlinearity on the whole axis”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, 2,  54–73  mathnet
3. Kh. A. Khachatryan, “On the solubility of certain classes of non-linear integral equations in $p$-adic string theory”, Izv. RAN. Ser. Mat., 82:2 (2018),  172–193  mathnet  elib; Izv. Math., 82:2 (2018), 407–427  isi  scopus
4. Kh. A. Khachatryan, H. S. Petrosyan, “One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, 6,  48–62  mathnet; Russian Math. (Iz. VUZ), 62:6 (2018), 43–55  isi  scopus
5. Kh. A. Khachatryan, “On the solvability of a boundary value problem in $ p$-adic string theory”, Tr. Mosk. Mat. Obs., 79:1 (2018),  117–132  mathnet  elib; Trans. Moscow Math. Soc., 2018, 101–115  scopus
6. Kh. A. Khachatryan, H. S. Petrosyan, M. H. Avetisyan, “Solvability issues for a class of convolution type nonlinear integral equations in $\mathbb {R}^n$”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:3 (2018),  247–262  mathnet  elib
7. A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear integral equation in dynamical string theory”, TMF, 195:1 (2018),  44–53  mathnet  elib; Theoret. and Math. Phys., 195:1 (2018), 529–537  isi  scopus
8. S. M. Andriyan, A. K. Kroyan, Kh. A. Khachatryan, “On solvability of class of nonlinear integral equations in $p$-adic string theory”, Ufimsk. Mat. Zh., 10:4 (2018),  12–23  mathnet; Ufa Math. J., 10:4 (2018), 12–23  isi
2017
9. Kh. A. Khachatryan, T. H. Sardaryan, “On solvability of one class of Urysohn type nonlinear integral equation on the whole line”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 17:1 (2017),  40–50  mathnet  elib
10. Kh. A. Khachatryan, “On the solvability of one class of two-dimensional Urysohn integral equations”, Mat. Tr., 20:2 (2017),  193–205  mathnet  elib; Siberian Adv. Math., 28:3 (2018), 166–174  scopus
11. 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)”, Uspekhi Mat. Nauk, 72:3(435) (2017),  191–192  mathnet  mathscinet  elib; Russian Math. Surveys, 72:3 (2017), 571–573  isi  scopus
12. Kh. A. Khachatryan, H. S. Petrosyan, A. A. Sisakyan, “On the nontrivial solvability of one class of nonlinear integral equations of the Urysohn type”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:2 (2017),  266–273  mathnet  elib
13. Kh. A. Khachatryan, M. H. Avetisyan, “On solvability of an infinite nonlinear system of algebraic equations with Teoplitz–Hankel matrices”, Proceedings of the YSU, Physical and Mathematial Scineces, 51:2 (2017),  158–167  mathnet
14. Kh. A. Khachatryan, H. S. Petrosyan, “One parameter families of positive solutions of some classes of convolution type nonlinear integral equations”, Sib. J. Pure and Appl. Math., 17:1 (2017),  91–108  mathnet; J. Math. Sci., 231:2 (2018), 153–167
2016
15. A. Kh. Khachatryan, Kh. A. Khachatryan, “Some problems concerning the solvability of the nonlinear stationary Boltzmann equation in the framework of the BGK model”, Tr. Mosk. Mat. Obs., 77:1 (2016),  103–130  mathnet  elib; Trans. Moscow Math. Soc., 77 (2016), 87–106  scopus
16. A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear model Boltzmann equation in the problem of a plane shock wave”, TMF, 189:2 (2016),  239–255  mathnet  mathscinet  elib; Theoret. and Math. Phys., 189:2 (2016), 1609–1623  isi  scopus
17. H. H. Azizyan, Kh. A. Khachatryan, “One-parametric family of positive solutions for a class of nonlinear discrete Hammerstein–Volterra equations”, Ufimsk. Mat. Zh., 8:1 (2016),  15–21  mathnet  elib; Ufa Math. J., 8:1 (2016), 13–19  isi  scopus
18. Kh. A. Khachatryan, Ts. E. Terjyan, M. F. Broyan, “On solvability of a Hammerstein–Voltera type nonlinear system of integral equations in critical case”, Vladikavkaz. Mat. Zh., 18:4 (2016),  71–79  mathnet
2015
19. A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear integral equation arising in kinetic theory”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, 2,  36–41  mathnet
20. 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. RAN. Ser. Mat., 79:2 (2015),  205–224  mathnet  mathscinet  zmath  elib; Izv. Math., 79:2 (2015), 411–430  isi  scopus
21. Aghavard Kh. Khachatryan, Khachatur A. Khachatryan, Tigran H. Sardaryan, “On solvability of one class of nonlinear integral-differential equation with Hammerstein non-compact operator arising in a theory of income distribution”, J. Sib. Fed. Univ. Math. Phys., 8:4 (2015),  416–425  mathnet
22. K. A. Khachatryan, T. E. Terdzhyan, “On the solvability of one class of nonlinear integral equations in $L_1(0,+\infty)$”, Mat. Tr., 18:1 (2015),  190–200  mathnet  mathscinet  elib; Siberian Adv. Math., 25:4 (2015), 268–275
2014
23. A. Kh. Khachatryan, Kh. A. Khachatryan, T. H. Sardaryan, “On One Nonlinear Boundary-Value Problem in Kinetic Theory of Gases”, Zh. Mat. Fiz. Anal. Geom., 10:3 (2014),  320–327  mathnet  mathscinet  isi
24. Kh. A. Khachatryan, “On positive solutions of one class of nonlinear integral equations of Hammerstein–Nemytskiĭ type on the whole axis”, Tr. Mosk. Mat. Obs., 75:1 (2014),  1–14  mathnet  elib; Trans. Moscow Math. Soc., 75 (2014), 1–12  scopus
25. A. Kh. Khachatryan, Kh. A. Khachatryan, “Qualitative difference between solutions of stationary model Boltzmann equations in the linear and nonlinear cases”, TMF, 180:2 (2014),  272–288  mathnet  mathscinet  elib; Theoret. and Math. Phys., 180:2 (2014), 990–1004  isi  elib  scopus
26. Kh. A. Khachatryan, T. H. Sardaryan, “On solvability of a class of nonlinear integral equations with Hammerstein type noncompact operator in the space $L_1(R^+)$”, Proceedings of the YSU, Physical and Mathematial Scineces, 2014, 3,  16–23  mathnet
2013
27. Khachatur A. Khachatryan, Tsolak E. Terdjyan, Haykanush S. Petrosyan, “On the solvability of one class of boundary-value problems for non-linear integro-differential equation in kinetic theory of plazma”, J. Sib. Fed. Univ. Math. Phys., 6:4 (2013),  451–461  mathnet
28. Kh. A. Khachatryan, “On solution of a system of Hammerstein–Nemitskii type nonlinear integral equations on whole axis”, Tr. Inst. Mat., 21:2 (2013),  154–161  mathnet
29. Kh. A. Khachatryan, “On the solvability of an initial-boundary value problem for a nonlinear integro-differential equation with a noncompact operator of Hammerstein type”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:3 (2013),  308–315  mathnet  mathscinet  elib
30. M. F. Broyan, Kh. A. Khachatryan, “On some nonlinear integral and integro-differential equations with noncompact operators on positive half-line”, Ufimsk. Mat. Zh., 5:2 (2013),  31–42  mathnet  mathscinet  elib; Ufa Math. J., 5:2 (2013), 31–42
31. Kh. A. Khachatryan, T. H. Sardaryan, “Solution of one Volterra type nonlinear integral equation on positive semi-axis”, Proceedings of the YSU, Physical and Mathematial Scineces, 2013, 3,  12–17  mathnet
32. Kh. A. Khachatryan, “On some classes of nonlinear integral equations with noncompact operators”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013),  181–188  mathnet
2012
33. Kh. A. Khachatryan, “On solvability one Hammerstein–Nemitski type nonlinear integral differential equation with noncompact operator in $W_1^1(\mathbb R^+)$”, Algebra i Analiz, 24:1 (2012),  223–247  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 24:1 (2013), 167–183  isi  scopus
34. Kh. A. Khachatryan, “On a class of integral equations of Urysohn type with strong non-linearity”, Izv. RAN. Ser. Mat., 76:1 (2012),  173–200  mathnet  mathscinet  zmath  elib; Izv. Math., 76:1 (2012), 163–189  isi  elib  scopus
35. Kh. A. Khachatryan, “Nontrivial solvability of a class of nonlinear integro-differential equations of second order”, Mat. Tr., 15:2 (2012),  172–193  mathnet  mathscinet  elib; Siberian Adv. Math., 23:4 (2013), 234–249
36. A. Kh. Khachatryan, Kh. A. Khachatryan, “Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases”, TMF, 172:3 (2012),  497–504  mathnet  mathscinet  elib; Theoret. and Math. Phys., 172:3 (2012), 1315–1320  isi  elib  scopus
37. Kh. A. Khachatryan, S. A. Grigoryan, “On nontrivial solvability of a nonlinear Hammerstein–Volterra type integral equation”, Vladikavkaz. Mat. Zh., 14:2 (2012),  57–66  mathnet
2011
38. A. Khachatryan, Kh. Khachatryan, “On solvability of a nonlinear problem in theory of income distribution”, Eurasian Math. J., 2:2 (2011),  75–88  mathnet  mathscinet  zmath
39. Kh. A. Khachatryan, E. A. Khachatryan, “Solvability of some classes of nonlinear integro-differential equations with noncompact operator”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, 1,  91–100  mathnet  mathscinet; Russian Math. (Iz. VUZ), 55:1 (2011), 79–87  scopus
40. Kh. A. Khachatryan, “On solvability of one class high-order nonlinear integro-differential equations with Hammerstein type noncompact integral operator”, Ufimsk. Mat. Zh., 3:1 (2011),  103–112  mathnet  zmath; Ufa Math. J., 3:1 (2011), 101–110
2010
41. A. Kh. Khachatryan, Kh. A. Khachatryan, “On solvability of one class of Hammerstein nonlinear integral equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, 2,  67–83  mathnet  mathscinet  zmath
42. Kh. A. Khachatryan, “Solubility of a class of second-order integro-differential equations with monotone non-linearity on a semi-axis”, Izv. RAN. Ser. Mat., 74:5 (2010),  191–204  mathnet  mathscinet  zmath  elib; Izv. Math., 74:5 (2010), 1069–1082  isi  elib  scopus
43. A. Kh. Khachatryan, Kh. A. Khachatryan, “A nonlinear integral equation of Hammerstein type with a noncompact operator”, Mat. Sb., 201:4 (2010),  125–136  mathnet  mathscinet  zmath  elib; Sb. Math., 201:4 (2010), 595–606  isi  elib  scopus
44. Kh. A. Khachatryan, “On solvability of some classes of Urysohn nonlinear integral equations with noncompact operators”, Ufimsk. Mat. Zh., 2:2 (2010),  102–117  mathnet  zmath
45. Kh. A. Khachatryan, “On one Urysohn type nonlinear integral equation with noncompact operator”, Proceedings of the YSU, Physical and Mathematial Scineces, 2010, 3,  23–28  mathnet
46. A. Kh. Khachatryan, Kh. A. Khachatryan, “On the solvability of a nonlinear integro-differential equation arising in the income distribution problem”, Zh. Vychisl. Mat. Mat. Fiz., 50:10 (2010),  1793–1802  mathnet  elib; Comput. Math. Math. Phys., 50:10 (2010), 1702–1711  isi  scopus
2009
47. Kh. A. Khachatryan, “Sufficient conditions for the solvability of the Uryson integral equation on a half-axis”, Dokl. Akad. Nauk, 425:4 (2009),  462–465  mathnet  mathscinet  elib
2008
48. Kh. A. Khachatryan, “Solvability of a Class of Integro-Differential Equations of First Order with Variable Coefficients”, Mat. Zametki, 83:6 (2008),  933–940  mathnet  mathscinet  zmath; Math. Notes, 83:6 (2008), 851–857  isi  scopus
2003
49. Kh. A. Khachatryan, “The etimation of one Volterian type integral equation”, Proceedings of the YSU, Physical and Mathematial Scineces, 2003, 1,  21–26  mathnet
2002
50. Kh. A. Khachatryan, “Application of the albedo shifting method to an integral equation”, Zh. Vychisl. Mat. Mat. Fiz., 42:6 (2002),  905–912  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 42:6 (2002), 870–877

Presentations in Math-Net.Ru
1. On solvability of some classes convolution type nonlinear multidimensional integral equations
Kh. A. Khachatryan, A. Kh. Khachatryan
Internaional conference «Modern Mathematical Physics. Vladimirov-95»
November 15, 2018 11:00   
2. Теорема существования однопараметрических семейств нетривиальных решений для некоторых классов нелинейных уравнений в $p$-адической теории струны
A. Kh. Khachatryan, Kh. A. Khachatryan
International Conference of Mathematical Physics dedicated to the memory of academician V. S. Vladimirov
November 9, 2017 14:00   
3. Вопросы разрешимости некоторых интегральных уравнений в теории $p$-адической струны
Kh. A. Khachatryan
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
November 24, 2016 11:00
4. О разрешимости некоторых нелинейных интегральных уравнений типа свертки
Kh. A. Khachatryan
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
September 24, 2015 11:00
5. О некоторых нелинейных интегральных уравнениях типа Гаммерштейна–Немыцкого на полуоси и на всей прямой
Kh. A. Khachatryan
Conference "Mathematical Physics. Vladimirov-90" dedicated to the 90th anniversary of academician V. S. Vladimirov
November 13, 2013 18:30   
6. О положительных решениях для некоторых классов нелинейных интегральных уравнений типа Урысона на полуоси
Kh. A. Khachatryan
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
May 20, 2010 11:00
7. О некоторых классах нелинейных и интегро-дифференциальных уравнений с некомпактным оператором
Kh. A. Khachatryan
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
February 19, 2009 11:00
8. Some integral equations of Uryson and Hammerstein type on the half-axis
Kh. A. Khachatryan
Second Russian-Armenian Workshop on Mathematical Physics, Complex Analysis and Related Topics
October 9, 2008 14:40   

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