# Heat equation with mixed boundary conditions

• October 25th 2010, 07:22 AM
Hasan
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
$u_x(0,t)=0$
$u_x(1,t)=\epsilon u(1,t)$
• October 25th 2010, 08:59 AM
Pandevil1990
What exactly is ε?A simple constant?Do we know something about it?
• October 26th 2010, 09:33 AM
zzzoak
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).