= Fundamental diffusion mode
{title2=$T(x,t)=e^{-\nu_0t}R_0(x)$}
For a <diffusion equation> with fixed homogeneous <boundary conditions>, a fundamental diffusion mode is an <eigenfunction> of its nonnegative decay operator belonging to the smallest decay <eigenvalue> $\nu_0$, when such an <eigenvalue> exists. It is the slowest decaying separated <normal mode>. With a discrete <spectrum> and an isolated lowest <eigenvalue>, initial data having a nonzero projection onto its <eigenspace> approach this decay law at late times. Strongly vanishing <thermal diffusivity> can destroy existence of a lowest mode, as illustrated by the <loss of a spectral gap under strongly degenerate radial diffusion>.
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