Question: reverse solution of diffusion equation

Hello all

I am going to find the diffusion constant in the following equation :


In a way that ,

evalf(Int(C(x,t=specific),x=0..L))/L - m_number(t=specific)=0

In other words, It would be an iterative procedure to guess "d" and then find the solution C (something like shooting method). The objective is to find "d" in a way that the average of C (solution of PDE) would be equal to m_number at that specific time.

Also, Since I have 5 specific time and m_number, I will have 5 different d. So, I need to use least square method or other optimization technique find one finalized d value.

I have uploaded my code.

I am not good at using Proc command and  I think the error of my code is because of that.

Would you help me to find out my problem in the code and any new idea for solviong this equaltion would be greatly appreciated.

Thank you for your kind attentions in advance




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