PDE with time-dependent boundary conditions

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Can anybody give hints how to solve the attached problem?
Peter Nave
Peter Nave on 1 Sep 2020
Thank you very much. I will study your codes and I will let you know how I fared.

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Accepted Answer

Bill Greene
Bill Greene on 1 Sep 2020
I do not believe it is possible to solve this problem with pdepe.
However I have written a one-dimensional PDE solver which is similar to
pdepe (similar syntax and runs in MATLAB)
but contains some enhancements including the capability to couple a
set of ODE with the set of PDE. These ODE can be used, for example, to model
the two reservoirs at the ends of your diffusion region.
My PDE solver can be downloaded here.
I have also tried to create a rough example that is similar to yours.
This example can be downloaded here.

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