On some classes of coefficient inverse problems for parabolic systems of equations with the ovedetermination date of evolutionary type

The article is devoted to the question of wellposedness in the Sobolev spaces of inverse problems on determining the righthand side and coefficients in a parabolic system of equations. The overdetermination conditions are the values of a part of the vector of solutions on some system of surfaces. Under special conditions on the boundary operators the local existence theorem of solutions to the problem is established.