Bulletin of TICMI 13

(3) u 0=u1=0.

The stability, weak and strong convergences have been proved.

R e f e r e n c e s

[1] G. Chichua, On a Boundary-contact Problem for a Solid-Fluid Model, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, 1995, v. 10, N1, 18-20 pp.

INVESTIGATION AND NUMERICAL SOLUTION OF ONE

INITIAL-BOUNDARY VALUE PROBLEM FOR

CHARNEY REGULARIZED EQUATION

 N. Iremadze, T. Jangveladze Medical Board of Georgian Defence Ministry I. Vekua Institute of Applied Mathematics I. Javakhishvili Tbilisi State University

In the cylinder Q=W x(0,T), where W is a rectangle {(x,y):0<x<l1, 0<y<l2} with the boundary W and T is a positive real number, there is considered the following initial-boundary value problem:

 (1)

(2)   U(x,y,t)=0, (x,y,t)Î W x[0,T],

(3)   D U(x,y,t)=0, (x,y,t) Î W x[0,T],

(4)   U(x,y,0)=U(x,y), (x,y)Î W .

Here D is the Laplace operator with respect to variables x,y, D 2 =D D , J is the Jacobian, b ,v=const>0 and U0 is a known function.

The equation (1) without the term vD 2U is called the Charney equation. Such a type of equations arises in the investigation of atmospheric motions. Note that (1) model some other physical problems.

Following to J.-L. Lions the existence and uniqueness of the solution of the problem (1)-(4) is proved.

It is also investigated the difference scheme

 (5)

(6)   u(x,y,t)=0, (x,y,t)Î w x w t ,

(7)   D u(x,y,t)=0, (x,y,t)Î w x w t ,

(8)   u(x,y,0)=U0(x,y), (x,y)Î v .

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