TY - JOUR
AU - Dairbayeva, G.
PY - 2018/08/24
Y2 - 2024/10/13
TI - The Cauchy problem for the Stokes equations
JF - Journal of Mathematics, Mechanics and Computer Science
JA - JMMCS
VL - 95
IS - 3
SE - Applied Mathematics
DO - 10.26577/jmmcs-2017-3-477
UR - https://bm.kaznu.kz/index.php/kaznu/article/view/477
SP - 78-89
AB - <p>In this paper we consider the Cauchy problem for the Stokes equations in domain with curvilinear<br>boundary, the solution is not known on a part of the boundary. This problem is ill-posed. Direct<br>and conjugate problems are constructed for the initial equations, the definition of generalized<br>solutions are introduced for these problems in the Sobolev space. It is shown that the solution for<br>the initial problem is reduced to the solution of the inverse problem for the direct problem. The<br>inverse problem is represented in operator form, objective functional is constructed, its gradient is<br>calculated. Computational algorithm is developed for solving the inverse problem for the Stokes<br>equations on the basis of the combination of optimization method and the finite element method<br>(FEM).</p>
ER -