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ABOUT SOME RETURN TASKS FOR ELLIPTICAL EQUATIONS Aliyev R. A. The Azerbaijan University of Cooperation Chair: "Information and economic information systems" Azerbaijan, AZE 1106, N.Narimanov 8b, tel.: (99412) 4360589, 5628745, e-mail:aramiz56@mail.ru The number of applied tasks is connected to definition of coefficients of an elliptical equation under some additional information on solution. In particular, definition heat physics environment characteristics in a stationary case leads to the return task for an elliptical equation. The return tasks for the queasy linear equations of elliptic type are considered in operations [1-2]. Let D ­ the bounded area n-dimensional evklid spaces En. x=(x1, x2, x3,... xn)- any point belonging D, ­ the border of area D assumed enough smooth and, = 1 + 2 , 0 , 1 - the set numbers. Q [ p0 , p1 ] . We will consider the task about definition from following conditions {kn (u ), q(u ), u ( x, p )} :

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i =1

n

ki (u )u

xi xi

+ q(u )u = h( x, p), x D, p Q pQ pQ

u ( x, p) | 1 = f1 ( , p), 1 , u1 ( x, p ) | 2 = f 2 ( , p ), 2 ,

kn ( F1 ) u 2 (1 , p) = g1 ( p),

pQ pQ

kn ( F2 ) u 2 ( 2 , p) = q( F2 ) ( p) + g 2 ( p),

where i = 1,2 ­ the fixed points the set functions, 1 , Fi = Fi ( p) = f1 (i , p), i = 1, 2, h( x, y ), f1 ( , p), f 2 ( , p), ( p ), gi ( p ), i = 1, 2, ki (u ), i = 1, 2, ..., n - 1, 0 < k i (u ) C1+ [ R1 , R2 ], i=1, 2,...,n-1, h(x, p), at any belong p Q according to spaces C ( D), C2 + ( 1 ), C1+ ( 2 ) and on p belong C (Q), gi ( p) C (Q), i = 1,2, ( P ) C (Q), 1 ­ a direction of an external normal to boundary 2, 2 ­ a direction of an internal normal to boundary i , i = 1,2 u u 2 ( i , p) = ( i , p), i = 1,2 in point R1, R2 ­ some numbers. Let's assume that functions 2 Fi ( p), i = 1,2 have opposites i ( Fi ), i = 1,2 defined on [R1, R2] in the field of value on Q and belongings (Q) . The thesis is devoted to research of questions of a correctness of this class of return tasks for elliptical equations.
References 1. Iskenderov A.D. The return task about definition of coefficients of a quasilinear elliptical equation.//Izv. AN Az. SSR. 2, s.80-85. 2. Klibanov M.V. Uniqueness as a whole return tasks for one class of the differential equations.//Dif.uravnenija.1984. .20, 11, s.1947-1953.
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