L E V V A S I L ' E V I C H O V S Y A N N I K O V ( O N H I S

F I F T I E T H B I R T H D A Y )

April 22, 1969 was the 50th bi r thday of the impor tan t Soviet mathemat ic ian and exper t on mechanics , Corresponding Member of the Academy of Sciences of the USSR, Lev VasiUevich Ovsyarmlkov.

Lev Vas i l ' ev ich was bern in the town V a s i l ' s u r s k in the Gor 'kovsk~i region. His fafl~er was a land s u r v e y o r and his mothe r a vi l lage teacher . In 1937 Lev Vas i l ' evyich entered the Moscow State Univers i ty where he studied until the s t a r t of the war . During the f i r s t months of the war Lev Vasi l 'evich worked on the cons t ruc t ion of defences. In the autumn of 1941 he completed his un ivers i ty course and went as a s tu- dent of the Leningrad Air Force Academy. In 1949 Lev Vas i l ' ev ich defended his candidate ' s d i sser ta t ion " Inves t iga t ion of gas flows with a s t ra igh t sonic l ine." During the period 1949-1953 Lev Vasi l 'evich work - ed a t the Ai r Force Academy and at the s ame t ime at the Leningrad Universi ty . F rom 1953 to 1956 Lev VasI I ' ev ich was occupied wlth scient i f ic r e s e a r c h in the field of applied ma themat ic s in Moscow. In 1956 he became a r e a d e r at the Moscow Physicotechnlcal Institute; in 1959 he left this position to work with the Siberian Division of the Academy of Sciences of the USSR, which had only just been organizcd. Thls m a r k - ed the c o m m e n c e m e n t of a t e n - y e a r per iod of fruitful scient i f ic , pedagogical , and organizat ional act ivi ty of Lev Vasi l ' ev ich , which st i l l continues.

At f i r s t he was a Senior Scientific Worker and then f rom 1961-he has d i r ec t ed the theoret ical division of the Inst i tute of Hydrodynamics . In 1961 Lev Vas i l ' ev ieh defended his doctoral d i sser ta t ion "Group p ro - pe r t l e s of d i f ferent ia l equations."

At the s ame t ime Lev Vas i l ' ev ich has played an impor tan t role at the Novosibi rsk State Univers i ty as P r o f e s s o r of the Chair of Differential Equations, d i rec t ing the Insti tute of Hydrod)mamics, and acting as Dean of the Mathemat ics Faculty.

In 1964 I_ev Vasl l ' ev ich was e lec ted a Corresponding Member of the Academy of Sciences of the USSR_

The ma jo r i t y of the scient i f ic works of Lev Vas i l ' ev i ch fall under th ree headings. The f i r s t is the problem of gas dynamics and, in the f i r s t place, the invest igat ion of t ransonic flows. The second - which has been cons ide rab ly developed by the s tudies of Lev Vas i l ' ev ich - c o v e r s the group proper t i es of d i f f e r - ent ia l equations. The third contains works on unstable mot ions of a l iquidwith a f r ee boundary, which are among the f i r s t in this field.

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Trans la t ed f rom Sibirski i MatemaUcheski i Zhurnal, V0i. 10, No. 2, pp. 243-245, March-April, 1969.

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Among the important results of the f irs t cycle one may mention the follow/ng: the theorem that when there is an outflow of a subsor stream with a critical velocity, leveling on the surface takes place at a finite d/stance from the opening:, a theorem on the singularities which are exhibited by a gas flc~- on a straight sonic llne and its application to the calculation of jets ~Ith a strnight transition llne.

The investigation "On the Trlcoml problem in a class o f generalized solutions of the Daler-Darboux equation" (1953) should be mentioned especially; here a method ~as f i r s t proposed for constructing a c e r - tain complete system of partial solutions on the basis of which a numerical method of solution of a number of gas d)~namical problems was justified. As early as 1950 this method has been first used to calculate the morde flow around a wedge. In addition he obtained a new class of partial solutions of the hydrodynamical equation and a number of other results.

T h e investigations of L. V. OvsyanvJkov's second cycle contain a large number of very important re~l ts. Already in the first investigation of this cycle: "Groups and group-Hnvariant solutions of differ- enUaI equations" (1958) the possibility of effective study (within the framework of the classical theory of continuous transformation groups) of the group properties of systems of differential equations occurring In physics and mechanics was demonstrated. The first calculation was made of the largest transformation group which is admitted by the system of equations for the one-dimensional motion of a was. The excel>- tional importance of the value of T (the ratio of the specific heats) at which the group is enlarged was re - vealed. The following investigations gave a group classification of the equations of thermal conductivity, the gas dynamical equation of Chaplygin. and also of second order linear equations with any number of i n - dependent variables. In con~nectAon with Chaplygin's equation it was found, in particular, that all the pre- viously obtained "go.J" approximations of this equation can be obtained as special cases of this classif ies- t-Ion.

L. V. Ovzyannikov's results from the second cycle of investigations formed the content of his mono- graph "Group Propert ies of Differential Equations," which appeared In 1962.

The investigations In the third cycle were devoted to one of the most difficult problems of hydrcxly- namlcs. Here Lev Vasil'evich has given not only first results, but atso the very mathematical formula- tions of the problem. These include investigations on existence and uniqueness, on the sL'tbility and de te r - ruination of partial solutions of the problem of unstable motion of a liquid with a free boundary, and a num- ber of model problems. It is significant that for the investigation of these questions it was necessary to use, and sometimes even create, a new mathematical apparatus; we mention here the concept introduced by Lee Vasil'evtch of a singular operator in Baru~tch spaces.

The breath of the scientific interests of Lee Vasil'evich is shown by his works in varied fields of n~athematics and mathematical physics (we only mention here their titles): "General solution of equations ofa renormalizcd group" (I955), "Note on the calculation of tht~ trace of a nonnegative completely continuous opera to r" (19G7), "Equations of the dynamical convection of ~he sea ~ (1967), and "On the Carleman system in the kinetic theory of gases" (1957).

Lee Vasii'evich combines the talents" of a brilliant mathematician with wide erudition in the field of mechanics and mathematical physics and contilmes the grand tradition of Russian science in the field of applied mathematics.

The pedagogical activity of Lee Vasil'evieh is Very broad; we only mention his work at the Novosiblrsk State University. Being one of the first teachers of the Novosibirsk State University, he read a course of algebra in 1959. Students of several generations remember his courses on ordinary differential equations, equations of mathematical physics, gas dynamics, and special courses and special seminars. Lee Vasll '- evieh's lectures on gas dynamics and the group prol~rt ies of differential equations, published recently at the Novoslbirsk State University, immediately became a bibliographical rari ty. One should also mention Lee Vasil 'cvtch's work as the Director of the Theoretical Seminar of the Institute of Hydrodynamics. Every participant at this seminar knows what it means to obtain the praise of its director .

One must also mention Lee Vasil 'evich's important work as the chief editor of the periodical "Applied Mechanics and Classical Physics" (Prikladnaya Mekhanika I Tekhnteheskaya Fizika).

Lee Vasli'evtch has often represented Soviet science at International Congresses and at Conferences; In.particular, at the lntcrnat/onal Congresses of Mathematicians at Stockholm and Moscow and at the Inter- national Congresses on Applied Mechanics at Munich and Stanford.

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The services o! Lev Vasll'evtch have been recog~zed by State .A~-ards: by the Order of the Labor Bed Banner and by meck~ts.

On his 50th birthday Lev Vasll'evtch Is at the height of his creati~ae power. There is no doubt that he will continue to enrich c~r science with many discoveries.

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