Solution.

Assume a 1D model is sufficient (e.g., insulated rod): $$ u(x,0)=\left\lbrace \begin{array}{ll} U_L, & x < L/2\\ U_R,& x\geq L/2 \end{array}\right. $$ $$ \frac{\partial u}{\partial t} = \dfc \frac{\partial^2 u}{\partial x^2},\quad u(0,t)=U_L,\ u(L,t)=U_R$$