The solution of the first problem shows that the state, in which large-scale convective flow in the mantle occurs under lithospheric plates, is unstable and must bifurcate into another more stable state at which the lithospheric plates become mobile and plunge into the mantle at subduction zones. Two problems of convective stability for the lithosphere with the Andrade rheology are solved. Besides, the transient creep changes the elastic crust thickness estimated within the power-law rheology of the lithosphere. At the transient creep, the effective viscosity, found in the study of postglacial flows, differs significantly from the effective viscosity, which characterizes convective flow, since timescales of these flows are very different. Since plate tectonics allows only small deformations in lithospheric plates, creep of the lithosphere plates is transient whereas steady-state creep, described by non-Newtonian power-law rheological model, takes place in the underlying mantle. The transient creep at high temperatures is described by the Andrade rheological model. Laboratory experiments with rock samples show that transient creep, at which strain grows with time and strain rate decrease at constant stress, occurs while creep strains are sufficiently small.
