CFD Online Discussion Forums - PDE with a partial derivative calculated at a given value of an indipendent variable

Hi, I am quite new in Comsol, I have just solved few problems using the model wizard so far.
I am just wondering if it is possible to solve numerically the following problem.

$\frac{\partial u(x,t)}{\partial t}=\frac{\partial^2 u(x,t)}{\partial x^2}+S \left [ 1+\frac{\partial u(0,t)}{\partial x} \right ]\frac{\partial u(x,t)}{\partial x}$
with

$u(\infty,t)=0$
and
$u(x,0) =\exp \left ( -\frac{x^{2}}{\pi } \right )-x \, \text{erf}\left ( \frac{x}{\sqrt{\pi}} \right )$

Where

is a constant equal to 100. I am interested in integrating from

going from 0 to 5. As $x=\infty$ we can simply use

in this case. In particular, I do not know how to write the derivative of the dependent variable in

inside the equation (it is the term in the square brackets).
Many thanks in advance.