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Armenian Journal of Mathematics
Volume 3, Number 4, 2010, 142–151
A life, devoted to the science
In the city of Glendora (California, USA) a distinguished
scientist, one of the leaders of mathematics in Armenia, the
outstanding authority in the theory of the partial differen-
tial equations Nazareth Ervandovich Tovmasyan on July, 23rd,
2010 has passed away.
N.E. Tovmasyan was born in 1934 in the village Bjni of
Hrazdan region of Armenia. In 1951 he entered the physical
and mathematical faculty of the Yerevan state university and
in 1956 he graduated. N. E. Tovmasyan’s scientific activity has
begun since that year.
In 1956 he started his working career in the Institute of mathematics and mechan-
ics of Academy of Sciences of Armenia. The first Armenian academician-mathematician-
A.L. Shahinyan, who those years was the director of the institute, noticed something in new
junior research fellow and in 1959, aiming the development the theory of the differential
equations in Armenia , sends N.E.Tovmasyan to postgraduate studies in the Steklov Insti-
tute of mathematics and mechanics of the Academy of Sciences of the USSR. The supervisor
of N. E. Tovmasyan’s studies becames the world famous scientist Ilya Nestorovich Vekua. A
year later I. N. Vekua has been appointed to the rector position of recently organized univer-
sity of the Siberian Branch of the Academy of sciences of the USSR, and N. E. Tovmasyan
moved with him in the city of Novosibirsk and continued his postgraduate studies in the
Institute of hydrodynamics of the Siberian Branch of Academy of Sciences of the USSR.
Further, almost ten years’ period of the life in Novosibirsk, in the famous Academgorodok,
where many glorious pages were added to history of the Soviet science, followed. Those years
Tovmasyan worked with M. A. Lavrent’ev, I. N. Vekua, S. L. Sobolev, A. V. Bitzadze and
other outstanding Soviet scientists. In 1963 N.E.Tovmasyan completed his PhD thesis and
started his work in the Institute of mathematics of the Siberian branch of the Academy of
Sciences of the USSR first as junior research fellow, afterwards as senior staff scientist at the
division of the theory of functions. In 1967 N.E.Tovmasyan gots his doctor’s degree ”On the
theory of boundary value problems for elliptic systems of the second order.”
The scientific interests of Nazareth Ervandovich were formed during these years and
the basis of his further investigations has been laid. The first works (PhD) are devoted to
investigation of Laplace and Tricomi equations in classes of discontinuous functions. Explicit
formulas for the solution of the Dirichlet problem for these equations in suitable classes
142
of solutions and boundary functions have been received. The results received for Tricomi
equation with degeneration are of particular interest, because of important applications these
results have in the problems of gas dynamics (we shall note that N.E.Tovmasyan’s constant
interest to the solving of actual applied problems was originated since then).
N.E.Tovmasyan’s thesis for a doctor’s degree is devoted to the basic research of elliptic
boundary value problems. For the first time in his investigations integral representations
of solutions of the elliptic systems, convenient for the investigation of classical boundary
value problems had been received. Using these representations, Nazareth Ervandovich has
reduced the Dirichlet problem for weakly connected system of the second order elliptic equa-
tions to the equivalent Fredholm equation of the second kind. The particular importance
have the results of the dissertation about the boundary value problems, not obeying to the
known Shapiro-Lopatinsky normality condition. Before there was an opinion, that as such
problems are neither Noetherian and nor normally solvable, therefore investigation of these
problems is impossible. N.E.Tovmasyan had described a wide class of such problems which
in suitable classes of solutions and boundary data are correct, and had showed a method
of their solution. The received results had been reported on the first Soviet - American
mathematical symposium on the partial differential equations (Novosibirsk, 1963) and had
met by scientific community with greater interest.
N.E.Tovmasyan’s works were the essential contribution in just arisen then the theory of
elliptic boundary value problems. As academician S.L.Sobolev wrote, ” N.E.Tovmasyan has
carried out a number of deep original researches in the field of the theory of the equations
with partial derivatives. His researches have found a broad response among experts, both in
Soviet Union, and abroad”.
In 1969 by the invitation of the rector of the Yerevan Polytechnic Institute A. M. Gas-
paryan, Nazareth Ervandovich came back to Armenia and since then his creative life has
been inseparably linked with this institute (now the State Engineering University of Arme-
nia, SEUA). The sixties and seventies years of the last century were years of rapid growth
of the SEUA. The developing industry of the Soviet Armenia required the organization of
training of new specialties. Leading experts from all ends of the Soviet Union were invited,
new faculties were created. N.E.Tovmasyan upon his arrival had headed recently organized
chair of applied mathematics (subsequently chair of higher mathematics No 2) over which
he supervised till 1990. These years the other side of his multifaceted talent was brightly ex-
hibited. A remarkable pedagogical gift indissolubly connected scientific activity of Nazareth
Ervandovich with his work on education of the rising generation of scientists. Under his
supervision more than 20 candidate’s and 3 doctor’s degree theses were prepared. The great
many of his pupils work now in SEUA and in the Yerevan State University. Other mathe-
maticians, who have been attached to the school of N. E. Tovmasyan, work now in Israel,
Russia, Ukraine and Germany.
Between 1990 and 2007 N.E.Tovmasyan was a professor of department of mathematics
143
of the SEUA and the head of scientific project ” Boundary value problems and their ap-
plications”. In those years Prof. Tovmasyan actively developed the theory of the elliptic
differential equations. These in-depth studies, developing function-theoretic methods in the
theory of boundary value problems, were the basis of two monographs published by World
Scientific in English in 1994 and 1998.
Scientific and pedagogical activity of Prof. Tovmasyan has been recognized by scientific
community and the government of Armenia. In 2000 he has been elected as a corresponding
member of the National Academy of Sciences of Armenia, and in 2003 he was awarded the
rank of the Honored Science Worker of Republic of Armenia. The memory of Nazareth Er-
vandovich - the outstanding personality, a distinguished mathematician, the talented teacher
will remain in our hearts forever.
Editorial
Bibliography of N.E. Tovmasyan
n
144
145
146
43. Boundary value problems for partial differential equations and applications in elec-
trodynamics. World Scientific, Singapore - New-Jersey - London - Honk-Kong, 1994, pp.
250.
147
58. Boundary value problems for certain classes of non-linear ordinary differential equa-
tions with free boundary, Non-linear boundary value problems, vol.9, Donetsk, 1999, pp.185-
189.
148
75. coauthor V.H.Iricyan, Boundary value problems with free boundary for some class of
quasilinear differential equations. ”Boundary value problems” Inst. of Applied Mathematics
and Mechanics of the Ukrainian NA of Sciences, Donetsk, 2001, pp.207-212.
84. The flight of an aircraft along a given trajectory and optimal flight control. Topics
in Analysis and it’s Applications, NATO Science Series, Series 2, vol.147, Kluwer Academic
149
Publishers, 2004, pp.347-365.
91. On differential equations with singularities in a class of analytic functions. Int.Conf.
”Harmonic Analysis and Approximations III”. Abstracts, Yerevan, 2005, pp.73-74.
92. coauthor H.A.Babayan. On an effective solution of the Cauchy problem for one
class of nonlinear differential equations. Int.Conf. ”Nonlinear partial differential equations”.
Abstracts, Donetsk, 2005, p.106.
150
101. On a Defect Numbers of One-Side Hilbert Problem in Multiply-Connected Domains.
D. Banach Center Conference. Abstracts PDE, Warsaw UN 18-24, 2006, p.36.
151