On nonlocal problems for systems of parabolic equations

The initial boundary value problems for systems of two parabolic equations are studied when the conditions with respect to the time variable are given only for one of the unknown functions. The first problem is considered in the case where along with the initial data for one of the functions the value of the same function is given at the final moment of time. The other one is the problem where two nonlocal conditions with respect to time are known for the same function. The global existence and uniqueness of the solution to these problems are established.