Stationary solution
= Stationary solution
{title2=$\partial_tu=0$}
A stationary solution of an evolution <differential equation> is independent of time. Substituting $\partial_tu=0$ leaves the spatial <boundary value problem> that determines its profile. For an <ordinary differential equation> this is an <equilibrium>; for a <partial differential equation> it may vary in space. A stationary profile need not have zero <flux>, although zero <flux> is forced in a one-dimensional conserved system with reflecting endpoints.