Constant flux for a one-dimensional divergence-form equation
= Constant flux for a one-dimensional divergence-form equation
{title2=$a(x)u^{\prime}(x)=J$}
On an interval, the weak equation $(au^{\prime})^{\prime}=0$ makes $au^{\prime}$ constant almost everywhere. If $\lambda\leq a\leq\Lambda$, the derivative energy on concentric subintervals satisfies $E(r)\leq(\Lambda/\lambda)^2(r/R)E(R)$. This supplies <dyadic energy decay> even though a one-dimensional <annulus> is disconnected.