The heat conduction problem

Submitted by vic777 on Sat, 10/13/2007 - 22:48.

General questions

What is a solution for the initial boundary-value problem (using separation of variables method)?
$u_t=4u_x_x, 0<x<1, t>0;$
$u(x,0)=x^2(1-x), 0\le x\le1;$
$u(0,t)=0 ; u(1,t)=0 ;t\ge0$

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The heat conduction problem