Nonlocal problems for the equations of filtration of nonnewtonian fluids in porous media

The following nonlocal problems for equations of filtration of Oldroyd fluids (1) and Kelvin–Voight fluids (2) in porous media are studied: global classical solvability on the semiaxis $t\in\mathbb{R}^+$ initial boundary-value problems (1), (3), (4) and (2)–(4); global existence theorems of time periodic solutions of equations (1) and equations (2) with time periodic external force $f$.