Solution
= Solution
Choose the <stationary solution> $w''=0$ satisfying $w(0)=0$ and $kw'(L)=H$. Hence $\boxed{w(x)=Hx/k}$. Subtracting it gives the homogeneous problem
$$
\boxed{v_t=\nu v_{xx},\qquad v(0,t)=0,\qquad v_x(L,t)=0,\qquad v(x,0)=-\frac{Hx}k.}
$$
This <boundary lifting> leaves a <Dirichlet boundary condition> at one end and a <Neumann boundary condition> at the other, as in the <fixed-temperature and fixed-flux heat equation on an interval>.