= Heat kernel with constant absorption
{title2=$K_c(x,t)=e^{-ct}(4\pi t)^{-1/2}e^{-x^2/(4t)}$}
The displayed <fundamental solution> solves $u_t=u_{xx}-cu$ on the real line with a <Dirac delta> at the initial time. It is the ordinary <heat kernel> multiplied by $e^{-ct}$, because that factor removes the constant reaction term. Its <integral> is $e^{-ct}$ and it converges to the <Dirac delta> as $t\downarrow0$. Convolution with initial data gives the corresponding solution. For $c>0$ the total mass decays by absorption; for $c<0$ it grows instead.
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