SCIENTIFIC ABSTRACT OLEYNIK, N.V. - OLEYNIK, O.A.

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• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001238010013-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 99
• Document Creation Date: November 2, 2016
• Sequence Number: 13
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

Investigating the offset of strass
81/1123/6 I/ODD/020/16 14/035
AOD4/AIOJ
obtained during the testing of speolmars with keyways of different shapes. The
most expedient shape with a minlimm value of K 6- m 1.0 pro'ved to be ka3ways with
rectangular or semicircular cross sa3tlon having smooth'Junotions with the
specimen surface. There are 6 figures and 2 references.
[Abstract'er's note.- Complete tranblati:,:h"
j
1. Bernshteyn

S/137/60/OW/()3/3-0/013
Translation from: Referativnyy zhurn,Ll, Metallurgiya,
6238
Petergerya, D.M Oleyn!k, N.V.
77ne 3cale Effed In Oveiloading Alloyed Steel
Odessk. po3itekhn. in-t
TErN The authors investigated the effect of preliminary cyclic load on
metal creep depending on the absolute limensions of the specimen. Thojn-
vestigation was carried out on prelim!3ary normalized 30XH3A (30KhN3A)Iyalloyed
steel specimens of 7.52; 12.5; 20 and ?7 mm in diameter. The results were com-
pared to those obtained previously froo 45 steel tests. It was established that
the absolute dimensions represented a factor which affected strongly thc- fatigue
limit of the material and its overload strength. It is shown that the overload
resistance of steel grows with inorea3td absolute dimensions: the cyclic
durability, under similar relative ove-load, Increases with a larger diameter of
the specimens. It is ass=4d that tbe regularities determined may in principle
also be applied to other structural st-tel grades.

- OlOnTU, N.V.; MF-RGIMYA, D.H.
n
Most suitable shape of cyll:drical specimens for fatigue testi7
-1
In pure bending. Zav.lab. 26 no.2:210 '60. (MIRA 13:5
1. OdesBIdy politekhnichasky intitut.
(Steel--Testj~jg)

CERYM, B.T., S33TAT03R, Te.T.
Determining the weight cf fatigns teBting machinery* Zavolabo
26 no.5:609-610 160. (,MM 13 -. 7)
1. Cdesskiy politelthnicbDakly institut,
(7atigue-te4ting machines)

2~jW
B/122/61/000/010,'005/011
D221/D304
AJTHORB: Petergeryal D.E.t EnSineerp and Ojgynikx-JL,_V. Candi--
date of Technical Sciencesp Docent
TITLE.- On the influence of absolute sizes of a specii.--Pr
section on the magnitade of effective stress c.
trations during loads above the fatigue limit
PERIODICAL: Vestnik mashinostroye:iiya, no. 10, 1961, 52 - 34
TEXT: The authors quote results o.! investigations conce'!King th,=
effect of overloads on fatigue res:.Btance related to stress cori~ ti-
trations derived from experiments itith structural steels. Specim!.s
were made in steels 45 and 30XH3A .30YhN3A). Effective coefficier,Tlo
of stress concentrationg corresponi,ing to the horizontA
# portion of
fatigue curve are designated by K and in the region of limited
strenr.,,':i by K1. The present artic5ii tabulates data which demonstra-
0
le that 1he Inclination of fatigue curves for under4ot and large
specimens is greater t1W in the ci,se of small and plain samples~
The latter exhibit a ten Idency to r!se with an increase of diametn-.--
Card 1/4

29339 S/I 22/61/000/010/ 005/k.
On the influence of absolute D221/D304
oonfiriaingg therefore) the law which expresses the drop of il
higher overloads. it also reveals the effect of absolute size,3 -,f
a specimen section on the charactex of this reduction.
of X with length of lio and diameter of speciiuen were invfstii-a
-teda The abscissae of bends for plaLn sEanples, K, were small-,
ponding abscissae N' of urves for underCUT SpeCl'!--,
the corres gy
but at 3 = N's KI = X . Kesult's of ~, s3pi I a t iq-*jg K Iplu-:,ted ii,
0 Cr (Y 0,
log coordinates are sho*n in Fig. 1, Yurther analysis all._-,~s tii-,
law of changes of KI wish log N in ;he ranges O-N and N - N,
Cr 0
re
presented by approximation of lini~ar equ4tions. ConsequenTly, 1,111-
full, Curves Xd, = ffig can be assi.med as three oroken sections.
in ranges of O-N and N N' they fcllow
0 0
(!I q
10 K2
Where Xd-I is the coefficient of stresp concentration in the case of
Card 2 4

B/122/61/000/010/005/011
D221/I)304
life NO K ditto for life of Nlt q is the angular coefficient,
dI_
,which characteri2es the inclinatioit of the curve of the relation-
ship between the effective atreign itoncentration coefficient and log,
of life, q "2 "1 Computi'tion of the latter indicates
I g
that KI varieB more sharply betweei, NC) - no, than in the region
205 _ No) and that inclination of curves X-1 N increases with grea-
o,
~ter diameters of specimense The ex1ression for Kal which is quoted
belowp was based on the step Invi ol the left hand branch of the fa-
tigue curve ae given by D.N. Reuilletov (Ref. b: 8b. "Povyeheniye
prochnoBti detaley nashin" Izd. AN BSSR) 1949)o The deduction can
be understood from arbitrary curves of fatigue for plain and under-
cut srxaimens. There are 2 figuresp 2 tables and 6 refer-ences:
5 Soviet-bloc and 1 non-Boviet-bloo, The reference to the English-
language publication reads as follovs: H. Moore and D. Markoving
Proceedings of Amer.Soc.for Testing blater.t v,.42-44t 1942-1944#
Card 3/4 -

On the influence of absolute ...
Pigs I* Curves giving the relation-
ship between K' and IS N:
2 22
29 339 3/1 -61/COO/010/()05/011
D221Y1301
legends I - Specimens of steel 45
with diameter of 7*52 mm; 2 - ape-
cimens'of steel 45 with diameter of
30 mm; 3 - specimens of steel 30XhN
3A with diameter of 7.52 nm; 4 - ape
cinens of steel 30nN3A with a dia-
meter of 27 mm.
yPj zlpj ?.Vl 5W OWIP, 2e lei
Pht, 1. KPrBU* 3)SM MUMN 07 12
06PAUN R3 C-IMAN 45 Jk)12W1Tj)Dw 7,52 jim; 2- apasum ns
'ToAs 45 Arawsypia N vx: S - obpnum m3 cumm WXHBA an.
Wpb)l 7,bi AX; J - OOPS311M M3 c?*Ax BDXH3A ANIINCTPDU
27.ux.
Card 4/4

s/o32/61/027/001/022/037
B017/BO54
AUTRORS: Oleynik, K. V. and Si:tvanskiy, N. A.
TITLE: Reconstruction of the HY(NU) Machine for Program Tests
PERIODICAL: Zavodskaya laboratori~aj 1961, Vol. 27, No. 1, pp. 84-85
TEXT: By reconstruction of the HY(ZU) machine it is possible to determine
the balance of stress in samples dwing testing. Figures show longitudinal
and cross sections of the machine$ end the load mechanism is schematically
represented. The mechanism is simple, and can be successfully used for
iwastigationB taking account of the conditions a 2-01 - const. and
a 3-0 2 - -const., as well as for invastigations under the conditions
Cr 2/61 - const. and a3/Cy2- const. There are 4 figures.
ASSOCI.1,TION: Odesskiy polytekhnicheAiy institut (Odessa Polytechnic
Institute)
Card 1/1

Al. l/.
jb l , '. -

Cyclic Metal Strength (Ccint.) SOV16025
and growth of fatigue cracks, , i)c role of Pinatio ciroriatlon
in fatigue fracture, an accele: nted method of deterritning
fatigue strength, the plottlng of fatipie diagrams, and
various fatigue tent methodn. New data arc presented on the
sensitivity of htg~h-strenUth v ~-nl to ntrenn concentration,
the effect of stress conrentra ten on the criterion or ratigue
failure, the effect of the olzt fnetor on the ntrenlp,th of
imetal. under cyclic loads, and : eoulta of endurance tents of
various machine parts. Proble-tc connected with cyclic metal
toughness, Internal, friction, aid the effect of corrosion
media and temperature ca the f ktigue strength of metals are
also discussed. No personalit.e-5 are mentioned. Each article
Is accompanied by references, itostly Soviet.
TABLE OF COWEIRS:
NATURE OF 'ATIGUE FRAGrURE
Oding, 1. A. Difruslonleas Plechan am of Formation and Growth of
a Fatigue Crack
Card 21,P

Cyclic Metal Strength
EFFECT OF THE STiESS CONCENTRATION
AND THE SIZE FACT)R ON THE FATIGUE
STREIGTH
Oding, I. A.., and S. Ye. Gurevich. Notch Sensitivity of
High-Strength Steels Under Cyclic L)ad
N. V., and 1. S. Mezentsev, Effect of Stress
Concentration on Characteristics of the Summation of
Fatigue Damage
Gli3unan, L. A., and Ye. N. Kostrov. Effect of the Size
Factor on Resistance of Metals to Corrosion Fatigue
Markovets, M. P. Technological Theo:,y of the Size Factor
in Fatigue Tests
CYCLIC TOUGIRTE IS AND INTERNAL
FR1;',TION
Ynternal Friction End !Tt-rlength

1;496h
S/124/63/000/001/065/080
D234/D308
AUTHORS: Oleynik, N.V.1 and I-Alezentsev, I.S.
TITLE: Effect of stress concentration on the summation
characteristic of fatigue damage
PrURIODICAL: Referativnyy zhuinal, Mckhanika, no. 1, 1963, 74,
abstract IV575 On collection: Tsiklich. prochnost'
metallov. M., AV4 1962, 177-186)
In repeated single-step overloadings with sign-
changing bending with rotation of specim'en6 made of 40Y (401~h) steel
k.~ 01 1
smooth, %Ath shallOT.7 ring-shaTped j,roove, with three such grooves,
with a transverse hole, %Ath deep ringl-.~haped groove, with three such
grooves and with a deep and an un:.oading groove, the authors 'studied
the ef7fect of stress concentratioiL on the inclination of secondary
A eventually on the magnitude of
fatigue curves of special kind, ai.
accumulated cycle ratio a, detem.ned from
Card 1/3

S/124/63/000/001/065/080
Elffect of stress concentration ... D234/D308
LJO.2) q [13 + f7-2 M]
a CTJ
N 69~ M 4+0
where m a-.d q are cotangents of irclination angles,(inclination
indices) of -the primary and secon~.ary fatigue curves, o', and cy-2
are levels of two-step loading, C I> 0'2; ~ = nI/n2 is the pro-
graming factor, n, and n2 are th~ total numbers of cycles corres-
ponding to o-I and a respectively, N2 and L2 are normal durabili-
ties on the az leve? for'the pr4mary 13Ad secondary fatiguc curve
res-,-.)ectively. With increase of I:he effective coefficients of stress
concentration detenained with respect to the bas s of limited
(105, 3 x 105 and 7 x 105) and lona-term (5 x IN durability, the
accumulat.ed cycle ratio decreases from approx. 1.8 to 0.97. The de-
crease of a is the sharper the hij;her the overload level. Stress
Card 2/3

conccntration
S/124
,/63/000/OUI/065/080
D234/D308
Concentration decreases a in compar'.son with smooth specimens. '.Iith
lixgc overloads and strong stress concentrations a becomes smaller
C>
than 1.
Z-.&stracter's note: Complete trans',ation .
_7 .

OISYNIK, N,V,,-kaud.tekhn.naa, dotsmt; FETERGERYA, D~M., inzh.
Role of the scale effect in overloa-i tastir~-, -,~f :-- ta- I . Vt.3t.-
mashinostr. 42 no.1'3:20-23 Je 162. !~EFCA :15:--1
(Steel-Testing)

OLEYNIK, NeVe, kandotakinanauk., dotqsent
Role of stress concentration in caue of programaed heading.
Veat.mashinostr. 45 no.2:13-16 F 165.
WRIA 18:41 )

ZILIBMSMU., I.m.; oLMM,_~ ~rkLtak)
CaBID of skin lesimiB cauBad ': 7 the influence of chromi-am in
the printil
ng industry. Gjg.t, rada i prof.2ab. no.3-1:51+-55 261.
(mm 14au)
It Itkutokly moditBimikiy initit,.It.9 IrkutBkiy oblaotnoy kozbno-"
vmerologiebesldy dispanser.
(PRINTKRS-DISFMES AND HEMS.) (CMGM-TOXICMDGY)

OL--,YlllKp O.A.
G. Ficherals, problem. DokI. Ali S.SSR 157 no.6:1297-1300
Ag 164, (1,11RA 17:9)
1. Moskovok.1y gosudarBtvonnyy anivorsitot im. LomononoVa.
Predstavlono akademikom I.G. P)trovskim.

OIL-Mil-K-, 0. A.
noscow, 1947
Hoscow State Univ m Lomonosov, 1947
"On Dirichlet I s problem f or equa tions of ell T)ti--,tl type, " II,:.ttej,,,nLt Sbor, 24., No. 1, 1949
(RecId 29 Aor 47) 1

m3nax, 0. 1.
Cand. Physicomah Sci.
Dissertation., "Concerning tile Topology of Algebraic Curves on an Algebraic
Surf ace."
113150
Sci. Ron. InHt. of Hathemritics, Moveow Ordqr of Lenin Stnte U, imeni.
M. V. Lomonosov

U1.6YRiK, 0. A.
"Algebraic Curves on an Algebraic Surface,," M p. 14at. Vauk. Vol. 6 11o. 4 (44),
PP 193-220, 1951.
lu-1635, 16 Jan 52

OLEYMj 0. A.
MSR/N&tbw=tICs sArill ii tei, 21,Aus 51
"So cond Boundary-Value Problem for an FUWic-
Type Equation With Small Parameter In the Eighest
Dew~ivatives," 0. A. Oleynik
~"Ddk Ak Nauk SSSR" Vol 1=, No 5 735-737
Cowiders the r, oln U.e (x,y) of the e I 1~e (U) = f (x, y)
the condition dU/dp a FJP) on the lound-
exy ~O of the region G. Iwiestigates the behavior
of lie vh the sTmIl Iwameter e (greater than
~e.
_. 'I 'D - -Bu 'ad-by'! Paid 1. .
zero. baitt
ro) te t
Jun 51.
pejit)ViiiY ig
f

1. CLETTIK, 0. A.
2. USSR MID)
4. Differential Equations
7. "Differential equations in mathematical phy3ics." V. I. Levin, TU. T. Grosberg.
Reviewed by 0. A. Oleynik, Sov. kniga no. 11 19i2.
Q.. Monthly List of Russian Accessicns, Library of Congrass., February 1953. Uncla..-Ified.

OD"rNIX, 01A,
One class of discontinuous solutions to a quasi-limear equation
the first order. Nauch.dokI.vys.shkoly; riz.-mat.nauki no.1:91-98
I
(MITI 12:7)
Moslrovakiy gosudaretvennyj unl*voysite I in. V.V. Lomnosovab
(Differential equations Partial)

USM/%&~~ties Boundary-Valve- MWAVM i52,
-ftopertiet, of the Solutims'of Cert&ft Z4MWAU77',~
value Problems for Equations of the Elliptic Typ,
0. A. O"Ynik.. Moscov ,
'V~ftte~&t Stior" Vol (72), No I, pp 695-702
Da=n-ntratea the uniqueness and continuous
4--pemi-ence of the zoIns of certain boundary.-Waue
problems for tv of the elliptic type upon tho::
coeffs of the aq, its right part and bounaary
fuwtiou. Considers clifferential eqo of the forat.
UU) = tLik -U + ~iuxi + Cu !* f (sumed
over repeatea M68), vhere a,b,e axvd- f I are
functiono of the n independent varidbles x.
submittea l8 Tan 52.
41

,USSR/Matbematics Small Parameter, Jul/Aug,52
Elliptic.Type,
191liptic-Type, Equations Vith Small Parameter in
the 91gheat Derivatiesj" O.A. Oleynik' Moscovp
4kth~lnst imeni,Steklov, Acaa Sci USSR
")fttez&4,t Sbor" -Vol X)= (73), No 1, ~VP 104-117
Studies the behavior of the soins of the regular
e"iptic clfffe"htial.eq O(UXX4.u Aux + BUY
+ Cu = r(x,y), vith the conditi~xy;jt a(P)u wr(p)
~(%.i.o tbe deriv in -lirection of normal n; P is a
~point of boundary S)', 16 the case vhere-small para-
meter e tends to zero. The behavior of soIns of
the Diriehlet problem for this eq in small para~
meter e has been inveatigatecl by N. Levinson
(A=aiz crk math, 51, w6 2, ig5o, 428-445).
Sulmitt6d I Feb 52.

PA 237T92
USSR/Mathematics Small Par-eter Fov/Dec 52
"Bourdary-Value Problem for the Equation ey"
F(x,y,y) for Sinall e," 0. A. Oleynik, Misco-a,
and A. i. Zhizhina, MOSCOY
"Hatenat Sbor" Vol 31 (73), lio 3, pp 70! 1-717
study the behavior of the solution ye(x) of subm
ject eq as the small parameter e tends tit 0. Be-
write subject eq in the form: ey"+A(x,y);,' = -
f(X,y,y'), along with appropriate boundwv condi-
tions. The simpler case where f(x,y,y') equals
B(x,y) was considered by Coddington and Ievinson
("A boundary va3ue problem for a nonlinejx differ-
ential eq vitb a s - I -paramiit6r," Bull J Oner Matb
Soc, 58, -No 1 (102. 237T92

OLEYNIK" 0. A.
ussiR/mathematieB - Bman-Farameter 21 Jul 52
Problem
'Soundary-Value Problems for Equatiois With a
Small Parameter in the Highest Derivitives,"
0. A. Oleynik
"Dok A*k Nauk SSSR" Vol 85, No 3, PP 1,93-495
studies the behavior of the solno of boundary-
-value -problems of the elliptic and pixalolic type
for the case Ybere there is a small ]arameter ep-
silon in the higbeBt derivs; e(uxx-+U3y)+ A(x,y)'ax
+ 131x,y)uy + C(x.,y)u = f (i,y)., -with condition
un +au = 7. Submitted by Acad 1,. G. Petrovskiy
3 Mq 5R.
235T73

N 24OT87
0. A.
13. Doe 52
USSRiMthemtics - Elliptic Type
"Equations off the Elliptic Type Which De ;enerate
on the Boundary of the Region," 0. A. Oltynik,
Math Inst irrzeni Steklwi, Acad Sci USSR
"DAN SSSR" Vol 67, ',4o 6, PID 885-888
Studies the -oroblem of the existence and unique-
-ness of the soln u(X.,Y) bounded in regioi, D of
the following eq L(u) uxx-.-y7uy ~,I- b(x,y)
UX+C(x,y)u = 0 satisfying on the boundar3 the
.Au = f
condition u;~. , where derivative ug is in di
x-ection g at an acute angle to normal n c C the
boundary. Presented 'by Acad 1. G. Fetrav%kiy
-4 Oct 52. 2240T87

';,'ull Title:
0- PI.:ILTT:~T 7, L
T r,,: no !it ~nr- f. T il t 1,_- L - c
i-v,~ r
Pu~,)jj_ 5,;.Ii 11 ~ ~ ~,~ "
J ,_
or:!
of Tc-~IunJcn, ,-j
v IS,)53
E,-Iltoriai Stl~.f-r, - I-- o. co
COiItriII)IIt,,.)T..-, to ILI v
0.
1u -_bl!,~ co.
C,)v
in
.~nt
Stt~ IT114
for 195". Th-

,OI;EYNUj, 0. A.
noncerning EquationB with Partial Derivatives whicb C ontain a Small Faramter
vith Antecedent Derivatives..8 report given at the All-Univeisity Scientific Conference
"Lomoncsoy Lectureall., Moak, Un. Vest,,, No*B., 1953&
Translation U-7895., I Mar 56

lum-nn-C, 0. A.
"Bcourdax-y.~VL,Iue Problems for Partial Differential Equc t
With Sra-U Paramet-c?rs in the Laroest Derivatives, and the (E
Problen for NonlinCLr Equations in the Lz~rge." Dr Phys-1-fait
71oscm Order of Le-nin State U imeni !'A. V. Lomnosov, 19 No-
MY. 9 Uov 54)
Sur-wey of Scientific and Technical Dissertations Defended 0
Educational Institutions (2-1)
SO: Sm. No. 521, 2 Jun 55

OMMIX. D.A.
Mauchy's probloyin for nnA-21near differpi2tial. e4uttlonz VIO
d1zcnmt1==B Initial conditlowl Zadacba kosbi 111a nell-
nalrykb differentsiallmyM uravimnii s razryvrqni nachallnymi
uslovilami. Hn9kva,l2d-vo Akademii muk SSSR, 1954. 19 p.
(Differantial equations) OULA 8:11)

cumlK, 0. A.
"Elliptic-T~pe Equations Degenerating :,ri che Pz)uncai-j of t1w f(egicon,"
Uspekhi Matematicheskikh Nauk, Vol 8, IN* 2 154), PP 159-167.

4DISYNIX, 0. A.
NOn tbAD Caucby Problen for Nonlinear Equations in a Class of Discc'y-t,-1-UCw
Funotions-,71 Dokl. AN SSSR2 95j, pp. 451-4-541, 1954
The author is one of the putBtanding mathemat:.cianD of the USSR in the field
of partial differential equations. It is claimed that ~~i,, lo the cnly woum In the USSR
ever to have receiTed the degree of Dr. of Physico-Mathem itic-ZLI Sciences, and the fact that
she did so at the age of 29 is considered extraordinary. I
Translation of paper by Rana V 6c)29, in Libr=7

OLIONIN, O.A.; VJNTSBLI, T.D.
CaucIq prablem and the f Irst bmnaarr Yalue p vblem for a quaml li-
near equation of the paTabolic typeo DDkI. Al SSSR 97 no.4:605-61DS
Ag 154. OUMA 7:9)
1, Preastavieno akademikom I.G.Petrovskim.
(Mfferential equations, PaTtial)

OLM111, D.A.
- WWWAMJ~~'
15tability of the 39umann pro-olem. UBp. zmt. nwLk 11 mo.1:223-225
JA-7 236, ()Ma 9:6)
(Differantial equations, Partial.)

MJ-zCT VSSR/MLTIIEMATICS/Differential equations CARD 1/2 PG - 496
AUTEOR OIwTJNIK O.A.
TIT13 On discontinuous solutions of non-linea2 differential equations.
PERIODICAI Moklady Akad.Nauk 109, 1098-l')l (1956)
reviewed 1/1957 -
A bounded measurable function u(t,x) is denoted as t solution of the Cauchy
problem ZU r4~Vtixlu)
(1) + 0
U(0,1) - u0(z), t;~O - boundedly meastirElle,
1) for everv continuously differentiab2e function :F(t,x) which vanishes outside
of a finite region, the relation holds: +0D
'bf u(t,x) +-0 f dm dt + J"(CI'x) u (m) dx - 0,
j j [17-t -7-1 1 f 0
> 0
where the first integral is extended over the halfplazie t.>0;
2) for(ever finite domain D there exists a monotoniAy decreasing function
X(t) I t ), 01, where for two arbitrary points (t'X 1) WLd (tIX2) of D for t> 0
the inequation

Doklady Akad.Nauk 109, 1098-1101 (1956) CARD :/2 PG - 496
u(t,Xj) - U(t'X 2)
X 1 2 4, K(t)
is valid.
The author proves that the solution defined in this way exists for (1) and
is unique. For the function -P here it is assuned that it is defined for
t,x,u:?/O, that it has continuous derivatives of second order, where
0 is 1)ounded if u changes
0 and that yul (t,x,u) for all x and t >
'f Ulu >
in a finite interval.
INSTITUTION: Mathematical Institute of the Acadeny of Sciences.

~A Z-
25-7-6/51
AUTEORs 018Y331k, O.A., Doctor of Physico-Mathenatical Sciences, Professor
at-the Moscow -University
TITLE: Let Us Be Friends, Say the Youth of Al'L Continents (Budem
druzhit" govorit molode2h, veakh kontLnentov)
PERIODICALt Nauka i Zhlznl# 1957P # 7, P 4 (USSR)
ABSTRAM Yjung students fTom many foreign countries attend schools In
he Soviet capital. When their studies are completed they re-
urn to their native countries, but t1ey do not forget their
former friends and teachers. When tallng part In conferences
and meetings abroad, the author notice,d that representatives
from all corners of the world got along fine. They love their
own countries and at the same time shtim sympathy toward the
others. To everyone, peace is dear. It is also a necessity for
the development and growth of science
The article contains one photo.
AVIILABLE: Library of Congress
CaTa 1/1

1. - ;
LI I- /.,
01MIX, O.A.
Discontinuous solutions of nonlinear differentlil equations
mat.nauk 12 no.3:3-73 HY-Je 157. i UBP;)
(MIR 0:1
(Differential equationi)

AUTHOR-s OLEYNIK'O.A. 42-6-11/17
TITLS: of the Generali2ed Solution of the Cauchy
Problem for a NonlimeaT System of Equationa Apyearing in the
19chanics (0 YoUnsivennosti obobahchenzogo reaheDiya 3adachi
Xoshi dlya odnoy nelinsynoy sistemy uravneziy, vatrechayusheheyaya
7 nekbanike)
PBRIODICALi Uepekbi Matematicheakikh Nauk,1957,VOI.12,lr.6,pp.169-176 (USSR)
AMSTRACTt The same method which the author bas alreaiy used in several
Papers f8ef-3t4-7for the consideration of iquations of first
order, here Is used for the investigation cf the equation
'j v ~u
+ 0, -~T - t7x
Z t
where %P I -e 0 in all arguments shall have cc ntinuOUB derivatives
T
of second order and 0. In the claBB of piecovise continuous
1P vv
functions which besides satisfy the condition u(t'x+O):!su(t'x-O)'
and in the class of bounded measurable functions (with the same
condition) the author proves the uniqueneso of the solution of
Card 1/2 the Cauchy problem.

On the UniqueneBa of the Generalized Solution of the Ca?ichy 42-6-11/17
Problem for a Nonlinear System of Equations Appearing it the
Nechanics
Five Soviet referenceB are quoted.
SUMMITTRI)i November 2, 1956
ITAILAILE: Library of Congress
Card 21r-

SUMBOT USSR/XLTBBMATIOB/3)i:f:ferentia1 equations 1.1RD 1/1 PO - 734
AUTHOR 013JMX O.A., VZNTZEI.T T.D.
TIM Thr first boundary valufa problem and the Cauchy problem for
quaBilinear equations of parabolic type.
MIODICAL Mat.Sbornik,n.Ser. _41, 105-128 (1957)
reviewed 5/1957
The present paper contains the proofs, the elaboration and some generali2ations
of the author's announcements in Doklady Akad.Nauk 17.L 6D5-6os (1954).
INSTITUTION: Moscow.

ALITHOR GLEYNIX O,A VVEDEMUYA N.D. PA - 3126
^; " c
'7 ~ ~'PLX u~;jo f tae CauckT Problem And the BDundar;' Value Preblen For Us
Nonlinear lqaations In A Cla3s of Unsvead.T Fanati*io,
(Reakenlyi zadachi W:mki i kraQTb-YCY 2adathi-dlya mj:Iineyrjk'A uravneniy 7
kJasse' razryvAftk fanktaiy -Russian)
MIODICAL DbklwV Akadsmii Nauk US!2,19557s Vol 113, Nr 3. PP 50-506
AD"iT,9d 6/1957 ArImad 7/1957
AB-STRUT Tke present paper XwniaboB the vorrtot So=latioi i~ of 09 Zaus)m. Problem
and t)ko boundary -value problem for tke epation &%- ?8t+44-(tp*.,u to=)
-& -~ 0 witkir a larp'domain w1t)k uns- isad7 iriltig- 60un-,
dar.7 condition. !~Jae general acluticm is dstsrmins~ kere ih "* #~rdme witk
Us p"r by OcAOIOIX=Xj, Mokl.".NauksVol 10�, & 6 (1956). Tkin prese3s
it aqui-ral'-nt to Us determination of tke general 3clution by Us ifitro-
duetion of a 'nyiniaking T13soaltr,, ie. tke bound &rj- .-value (ILI tke para-
MOUY & tends towBrd zero), -of take soIdtions of Us torrespond1mg problem Is
SouOt for t1a paraboliv equation f, a%/Ul-BU/a 4 ~ a? (tPjtS'U)/&+ T Noxqu)
1.) CUUCH114 Problem? T(t,9xjvu) aM T (tjx'9v) kave a teady derivationg of se-
cond ordere
U10 > =-a aer=sd to a0p17 and, uo(x) it assumed to be a limited
function me urabl* at aU. x. tt first tka geniara3hed solution ol C,%WHXIO
problem is jv~ for Us oquaiton written dcum abcre, Tkis generalized eclu-
91*
tion exist ar4l U'unique, jk furtkiai Usorem, is glien and yroved.
2,) Us Boun4wy Val-as Ilrbblens Tke aut)=B ex=Jne tNe boundary problem
Card 1/2 for,the e s4lon given above witia Us conditiorm u(t9O)-U)^)"

Ike Solution of Us Caucky Problem And Uke Boundary Value FA - 3126
Itr-oblem For tkt Nonlinear Zquatiow In A Class of Uz steady Functions o
u(t,,l)-uiM in ~C),oD for some quasilinear equationt
PERIODICALs Referativnyy zhurnal. Matematika, no. 10, 1961. 33-34,
abstract 10 B 153. ("Tr. Vaes. soveshchaniya po
differentsialln. ura-,rneniyam, 1958"- Yerevanj AN Arm SSR,
1960, 98-101)
TEXT: The authors consider the quasilinear equations
U + ?-T-Lul. ~ 'E VU
t --- ~) x '~ x2 C > 0
-4 u '~ 1P (u) 0
+ (2)
and the initial conditions
Card 1/4 ult-0 U o(2) CDU- for 1-> - OD , U 0(I)-> U f Or I OD (4)
Let T(u) be so that there exists a solution UIE (X-I-t) of (1) so ttiat
-P
u u for co )--~,u. for 4 CD
Let exist the integrals
00
[Uo(~) u.jd~ and ~ ET 10 U
-co X
Then there exists a solution ue (x-kt) of (1) so that
Co ["
5 U(~' 0
-00
Card 2/1[

32448
S/044/61/000/010/012/051
On the asymptotic behavior of the C111/C222
and there holds the
Theorem I : If the initial function u 0 (x) satisfies the above mentioned
postulates then, uniformly in x, the solution of the Cauchy problem for
?I) with t->co tends to the solution 'Ue (x--kt) which is dettermined
by (5). If for certain constants oL > 0 and M > 0 it holds kdditionally
lu0(x) u d~ !5 Ble
-00
OD
IU 0 00 U+j ds-< 111 e
then it holds
-St
I'U". (x - kt) - u. (t,x)l M
2
for all x and t, where
B> 0 , H 2> 0 - const.
Card 3/)f

3240
3/04 61/ooo/oiO/0'2/051
On the asymptotic behavior of the C11WC222
let
u- for
for p,(u+)
t
Let uE (t,x) be the solution of the problem (1), (3), (4) 11 '- < U+
~P"(u)> 0 . Then for t-.> oD , ur (t,x) tend s uniformly in% and i' tends to
H(x/t). And finally s If uC (t,x) is the solution of (1), (3), U(X,t,)
the solution of (2), (3), if u satisfies the conditlon~, (4) aid ii
u- ~ U = a , tpll(u)> 0 then it holds uni f ormly in x u x --~ a
u( a for t-a~co. Proofs are missing.
[Abstracter's note : Complete translation.-I
Card 4/4

3245D
/,6,25700
AUTHOR3 Oleyniko O.A.
S/044/61/000/010/0-4/051
C111/C222
TITLE: The solution of basic boundary value problems for equations
of second order with discontinuous coefficientd
PERIODICALs Referativnyy zhurnal. Iffatematiks, no. 10, 1961, 8,39,
abstract 10 B 170- ("Tr. Vses. soveshchaniya po
differentsialln. uravneniyam, 1956"- Yerevan, AN Arm SSR,
1960, 113-114)
TEXT: The author considers the elliptic equation
(a,,(x) u 0, a,j = aji
T _X'
X = (X,'..." X M aij (i) -- sufficiently smooth everywhere in the
region SL with a probable exception of points of certain snooth (n-!)-
dimensional manifolds in which the a ij may be diSCOntinUO'LS. These mani-
folds decompose rL into a finite number of regions
Card IN

The solution of basic boundary
32450
S/04#61/000/010/01~/051
C1111C222
k1 denotes the boundary of the regions SL k and SY It is assumed
1
that a . at both sides of has the boundary values a~- and ai~
ij k1 11 1)
The boundary S of rL is smooth. The author seeks a function u(x)
(classical solution of the Dirichlet problem) which is continious in
+ S and which in all points of T~ rkl ~ satisfies the equation L/
and the conditions
u1 f (2)
du a u
a -L- on F
k dNk I d1l1 k1
here f is a function given on S 0 ai > 0 const ; du/dNk ~ du/!Ni are
derivatives in the directions of the conormais of Besides.. the
generalized solution of the problem is considered, i,e. a u())6:"V2
which satisfies (2) and which is go that for every F(x)E ,Y(1, (J?-) which
2
Card 21+

3245o
The solution of basic boundary
vanishes on S the relation
aa ~ u ~-F d 11
It ii 21X Z Xj
S/044J61/000/010/01,-/051
C1111C222
- 0
is satisfied, where a is a function in1l which in the points of A-L
is equal to the constant a i . It is proved that the solution cf the
Dirichlet problem classical and generalized) is unique. Unde3 the same
assumptions for a JX) and a j(x) the author considers the first
boundary value problem and the Cauchy problem for the parabol-.c equation
u n
'>7 (4)
t . Z a (2) U
Jtj=l ( ij x
Likewise generalized solutions of the Cauchy problem and the nixed
problem can be obtained for a hyperbolic equation with discontinuous
coefficients ; furthermore the solution of the first boundary value
Card 3/4

32450
S1044J61 /000/0 10/0 1, /0 51
The solution of basic boundary ... CI1I/C222
problen amd the Cauchy problem for equations (4) in the case oere a 0 and 4
aij depend on t and i and have discontinuities on surfaces of ihe space
x being variable with the time (cf. R Zh Mat 1961, 7 B 205)-
[Abstracter's note : Complete translation -1
Card 4/4

ILIIII, A.M.; OMNU, O.A. (Xoskva)
As7mptotic behavior of solutions of the Caueby problem I)r
some quasilinear equations with large time values. Hat. sbor.
51 no.2:191-216 Je 160. (MIR& 13:9)
(Differential equations, Partial)

3-fo
86821
S/020/60/135/005/006/043
C111/C222
AUTHOR: Ole7nik,,gA.
TITLE. A Method for Solving the Generalized Stephan's Problen
PERIODICAL& boklady Akademii nauk SSSR, 1960, Vol.135, N0.5, :)P-1054-1057
TEXT: Let S be given constants kvalues of the tinDperature u
for which the state of aggregation of the medium changes). The points
Si(Si`-Si+1) divide the u-aiis into V+1 intervals. Let 1 1 be the i-th
interval. A continuous function u(t,x) defined in QtOz-.t~-~T, D-.enx