Initial - Boundary Value Problem

Submitted by vic777 on Sat, 11/17/2007 - 22:42.

What is the solution for this equation?
$u_t-u_x_x=2x^2, 0<x<1, t\ge0,<br /> u(x,o)=sin(\pi*x),<br /> u(0,t)=t,<br /> u_x(1,t)=1$