SCIENTIFIC ABSTRACT VENTTSEL, T.D. - VENULET, J.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001859410020-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 1, 2001
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

VENTTSELI, T.D.
Some quasi-linear parabolic systems with increasing coefficients.
Dokl. jUl SSSR 140 no.2;2PI&-28(. S 161. (MIRA 14:9)
1. Moskovskiy gosudarstvennyy universitet Im. M.V.Lomonosova.
Predstavleno akademikon I.O.Petrovskim.
(Boundary value problems) (Differential equations)

VENTTSELI, T.D.
- -1 , ~. . ....
Quasi-linear parabolic systems with growing coefficients.
Vest. Mosk. un. Ser. 1: Mat., mekh. 18 no.6;34-44 11-D'63.
OGRA 17s2)
1. Kafedra differentir.31'nykh uravneniy Moskovskogo universiteta.

28657
3/020/61/140/002/002/023
C111/C444
A-U-TR~R: Venttsell T. D.
TITLE; On some quasilinear parabolic systems with growing
coefficients
PERIODICAL: Akademiya nauk SSSR. Doklady, v. 140, no. 2, 1961,
284-286
TEXTt For the system
?2U ;)a -a T (u, V)
+
jt 9x
2v v (u,v)
F- _j_ +
Iax 2 zt ax
the following boundary value problem is considered
"1t-0 uo(,~, v1t.O - v 0(X)
Card ulx-x 1 U 1X-X = 0, V1 X=X Vi X-X . 0 (3)
YS 2 2

28657
S,/020J61/140/002/002/023
On some quasilinear parabolic systems ... C111/C444
assuming that (2) converges to a hyperbolic system of first order for
-4 0. The equation
qvF u - (1P - %yv) F v F - 0
u u u uvv (4)
ia of the same type like (2) for F, - 0.
Theorem 1: If (4) possesses a solution F(u,v) such that for all u,v
Fuu E2 + 2F uv + Fvv~ 2 >, dk (Ufv)(~2 + ~2 61 > 0 (6)
then
XA, X
F(u(x,T),v(x,T))dx F(u o(x), v0 (x)) dx (7)
I', I
Let B(M) max (1(f
n If
., 1)P
n
xItE R v
I Ul , IVI t,-M
Card 215

28657
3/02 61/140/002/002/023
On some quasilinear parabolic s,stemB ... ClIIYC444
B1 (M) - max (ID 291, 1 D 2,f
X, tr: R
ju.1,1VI 4 'M
where D2 is an arbitrary second derivative
f(jul ) - min(min F(u,v), min F(-u,v)),
v v
g(jvj ) = min(min F(U,V), min F(u, -v))
U, U.
R = R ~ x 1 :!& x 1S x 2 ' 0 "' t --- T
Theorem 2: The coefficients of (2) and the boundary functions are
assumed to satisfy 'the smoothne:~oconditions of theorem I of a former
paper of the author (Ref. 1: DAN 117, (1957)). The equation (4) is
supposed to have a solution F(u,v~-,satisfying (6) and
F(0,O) - FU. (0,0) - Pv(0,0) = 0 (9)
Card 3/S

28657
S102 611140100210021023
On some quasilinear parabolic systems.-.. C111YC444
and for which
M
B(M) + MBJ(M) - 0(f(s)),
B(M) + MB,(M) = 0(g(M))-
2
Then the problem (2), (3) possesses a'solution for all t.
one defines I(s) to increase like IsIp, if
k, Is I P