# Math Help - Heat equation with mixed boundary conditions

1. ## Heat equation with mixed boundary conditions

Does anyone know what is the solution of the heat equation
$u_t(x,t)=u_{xx}(x,t)$

with mixed boundary conditions
$u_x(0,t)=0$
$u_x(1,t)=\epsilon u(1,t)$

2. What exactly is ε?A simple constant?Do we know something about it?

3. At x=0 there is no flow of temperature.
At x=1 there is flow of temperature.

But there must be initial conditions: the initial distribution of temperature
u(x,0)=f(x) which changes in time due to flow of temperature (boundary conditions).
You may try to solve by separation of variables
u(x,t)=p(x)q(t).