# Intro to PDE: Related homogeneous boundary condtions

(partial derivatives didn't carry over well, so I just used a d)

1. Homework Statement
Give an example (as simple as possible) of a reference temperature distribution r = r(x, t) satisfying the following boundary conditions

DN: r(0, t) = A(t), (dr(L,t) / dx) = B(t);
NN: (dr(0,t) / dx) = A(t); (dr(L,t) / dx )= B(t);

For each of the above BC, compute the reference source function:

Qr(x, t) =dr / dt−d(^2)r / dx(^2) .

2. Homework Equations

I don't know if these are actually relevant.

v(x,t) = u(x,t) - r(x,t)
dv/dt = d(^2)v / dx(^2) + [Q(x,t) - dr / dt + d(^2)r / dt + d(^2)r / dx(^2)

3. The Attempt at a Solution

I basically just solved r for the boundary conditions then took the derivatives with respect to t and x to find Qr(x,t), but I don't know if that's right. My answer for the DN case of Qr ended up as : dA / dt + ( dB / dt )*x

Are solutions like that okay, or am I supposed to be doing something else?