The Green's function for the 1d Heat equation with Dirichlet BCs on the domain $(0,1)$ is
$$G(x,y,t) = 2\sum_{n=1}^\infty \sin(n\pi x)\sin(n\pi y)\exp(-n^2\pi^2t)$$
Is this function non-negative? Is there an easy proof for this?
2026-03-25 19:02:59.1774465379
Green's function for 1d heat equation on finite interval: is it non-negative?
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