  We consider the dynamics of semiflows of patterns on unbounded domains that
are equivariant under a noncompact group action. We exploit the unbounded
nature of the domain in a setting where there is a strong `global' norm and a
weak `local' norm. Relative equilibria whose group orbits are closed manifolds
for a compact group action need not be closed in a noncompact setting; the
closure of a group orbit of a solution can contain `co-solutions'.
  The main result of the paper is to show that co-solutions inherit stability
in the sense that co-solutions of a Lyapunov stable pattern are also stable
(but in a weaker sense). This means that the existence of a single group orbit
of stable relative equilibria may force the existence of quite distinct group
orbits of relative equilibria, and these are also stable. This is in contrast
to the case for finite dimensional dynamical systems where group orbits of
relative equilibria are typically isolated.
