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PDE with a partial derivative calculated at a given value of an indipendent variable

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November 30, 2023, 05:18	PDE with a partial derivative calculated at a given value of an indipendent variable	#1
umby1976 New Member roberto popov Join Date: Jul 2023 Posts: 2 Rep Power: 0	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.

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