u(0)=0; u(1)=1;

1) Heat equation in 1D: 
f(x)=-∂(λ(x)∂u/∂x)/∂x

2) f(x)=const=h; λ(x)=const=λ;

3) h= -λ*(∂u^2)/∂x^2

4) The second derivative: h= -λu”(x);