I have the following PDE with initial+boundary conditions:
$U_t = - U_{xx}$
$U(x,0) = 0$ for $x>0$ , $U(0,t) = 1$ , $U(1,t) = 0$.
The solution is for $0<x<1$ and $t>0$.
Is there an analytical solution for this PDE? I have tried solution by seperation of variables but it led me nowhere because of the boundary conditions. Thanks in advance