Advanced Engineering Mathematics, Lecture 5.2: Different boundary conditions for the heat equation

Advanced Engineering Mathematics, Lecture 5.2: Different boundary conditions for the heat equation.

In the previous lecture, we solved the heat equation under homogeneous Dirichlet boundary conditions: the temperature at the endpoints is fixed at u(0,t)=u(L,t)=0. In this lecture, we see that when the endpoints are inhomogeneous, we just add the homogeneous solution to the steady-state solution. Next, we consider von Neumann BCs, u_x(0,t)=u_x(L,t)=0, which occur when the endpoints are insulated. After that, we consider mixed boundary conditions, and then periodic boundary conditions, the latter of which are needed to model the heat equation on a circular wire.

[psychosis]

what if one of the rate of changes in boundary conditions is not zero? I couldn't find it anywhere on the internet :(