Does anyone know what is the solution of the heat equation

$\displaystyle u_t(x,t)=u_{xx}(x,t)$

with mixed boundary conditions

$\displaystyle u_x(0,t)=0$

$\displaystyle u_x(1,t)=\epsilon u(1,t)$

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- Oct 25th 2010, 07:22 AMHasanHeat equation with mixed boundary conditions
Does anyone know what is the solution of the heat equation

$\displaystyle u_t(x,t)=u_{xx}(x,t)$

with mixed boundary conditions

$\displaystyle u_x(0,t)=0$

$\displaystyle u_x(1,t)=\epsilon u(1,t)$ - Oct 25th 2010, 08:59 AMPandevil1990
What exactly is ε?A simple constant?Do we know something about it?

- Oct 26th 2010, 09:33 AMzzzoak
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).