PT Journal
AU Godunova, EK
   Levin, VI
TI Some general features of heat conduction
SO USSR Computational Mathematics and Mathematical Physics
JI USSR Computational Mathematics and Mathematical Physics
PY 1966
BP 212
EP 220
VL 6
IS 6
DI 10.1016/0041-5553(66)90173-X
DE mathematics; temperature distribution; rod
AB LET the initial temperature distribution in an infinite insulated rod without a heat source be given by a continuously differentiable function y = f(x), having a single maximum at x = 0 and two points of inflexion. The equation f′ = 0 then has a unique solution x = 0, where f′(x) > 0 for x < 0 and f′(x) < 0 for x > 0, We shall describe this as a one-hymped distribution. We shall assume that f/(x) also satisfies: (1) f(x) > 0 for − ∞ < x < ∞; (2) f(x) and x(fx) are integrable throughout the axis. Then the distribution remains one-humped for all t > 0.
ER