Question: (a) A separated-variable solution to the heat equation is U ( ~x ) = cos( lx )cos( my )cos( nz ) e pt . What

(a) A separated-variable solution to the heat equation is U(~x) = cos(lx)cos(my)cos(nz)ept.

What is p in terms of the wavevector?

(b)In 1 space dimension the heat equation is U/t = 2U/x2. Try the non-separatedvariable form: Ublob(t,x) = t1/2ex2/4t. This represents a localized blob of heat spreading out.

(c)In 2 space dimensions you can multiply the spreading blob solution in (b) with the same function Ublob(t,y) and get U2d blob(t,x,y) = t1e(x2+y2)/4t. Is this also a solution?

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