= Supersolution
For a <differential equation> $L[u]=0$ with its comparison order fixed, a <supersolution> satisfies $L[w]\geq0$. For example, if $L=\partial_t-\partial_x^2+Q$ with $Q\geq0$, a sufficiently regular $w$ satisfying $L[w]\geq0$ and dominating the initial and boundary data lies above a solution by the <parabolic comparison principle>. An unbounded-domain barrier such as $w=\eta e^{3t}(1+x^2)$ can provide the missing boundary control at large distance. The sign convention belongs to the chosen <differential operator> and must be stated.
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