Positive temperatures on a semi-infinite rod
David Vernon Widder · Transactions of the American Mathematical Society · 1953
D. V. WIDDER 1. Introduction.In these Transactions the author [1944; 85 ](2) showed that any solution u(x, t) of the heat equation d2u du(1.1) -= -dx2 dt which is non-negative for positive time and zero initially, w(x, 0+)=0, is identically zero.It was also proved that any solution non-negative for i>0 must have the form u(x, t) = (4x¿)-1/2 f e-2/4 00 [e-(x-v)2tu -e-^rflu]f(y)dy.