  The aim article is to contribute to the definition of a versatile language
for metastability in the context of partial differential equations of evolutive
type. A general framework suited for parabolic equations in one dimensional
bounded domains is proposed, based on choosing a family of approximate steady
states, and on the spectral properties of the linearized operators at such
states. The slow motion for solutions belonging to a cylindrical neighborhood
of the family of approximate steady states is analyzed by means of a system of
an ODE for the parameter $\xi$ that describes the family, coupled with a PDE
describing the evolution of the perturbation $v$.
  We state and prove a general result concerning the reduced system for the
couple $(\xi,v)$, called quasi-linearized system, obtained by disregarding the
nonlinear term in $v$, and we show how such approach suits to the prototypical
example of scalar viscous conservation laws with Dirichlet boundary condition
in a bounded one-dimensional interval with convex flux.
