On a non-linear non-stationary inverse problem of hydrodynamics

Abstract

The authors study an inverse problem for the non-linear non-stationary Navier-Stokes equations. This problem consists of finding vector-valued functions of the velocity, the pressure and the external force. An existence theorem is given both in two and three dimensions.

Simultaneous determination of time-dependent coefficients in the heat equation

“…the monographs of Prilepko et al [27] and Ivanchov [17]. In heat conduction for example, attention was paid to the unique solvability of one-dimensional inverse problems for the heat equation in the case when the unknown thermal coefficients are constant [4], time-dependent [15,16], space-dependent [1], or temperature-dependent, [20,23,24].…”

On the problem of determining the parameter of an elliptic equation in a Banach space

“…Theory and methods of solutions of inverse problems of determining the parameter of a partial differential equations have been extensively studied by several researchers (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein). It is important that several inverse problems of determining the parameter of partial differential equations can be reduced to nonlocal boundary value problems for partial differential equations (see [1][2][3][4][5][6][7][8][9][10][11] and the literature cited therein).…”

On source identification problem for a delay parabolic equation

“…Identification problems take an important place in applied sciences and engineering applications and have been studied by many authors (see [13][14][15][16][17][18][19][20] and the references given therein). Solving the direct problem permits the computation of various system outputs of physical interest.…”