# What is a quasistationary approximation

I was reading an article which states :

The linear-stability analysis for this system can be performed in complete generality; but it will be best for purposes of this review to go directly to what is called the "quasistationary" approximation. We are looking for a linear equation of motion for the interfacial position, $$z (\text{interface}) = \zeta(x,t)$$

Can anyone explain what does the author mean by "quasistationary approximation".

it turns out that the interface moves so slowly that it remains effectively stationary during the time needed for relaxation of the diffusion field. Thus it seems reasonable to solve the problem approximately by, first, solving the time-independent diffusion equation (3.6) subject to the thermodynamic boundary condition (3.4) on the quasistationary interface $$\zeta(x, t)$$, and then inserting this result into the continuity condition (3.2) to find an explicit expression for $$\partial \zeta /\partial t$$.