Dear Gianluca, dear Frank, gents,

You were both "spot-on". 1. The unboundedness of the domain was the problem. 2. And I would quickly have found that out if I had simplified the problem. For your entertainment I enclose the "corrected" Notebook, which shows that if I replace the upper limit by a large number, Mathematica finds the solution without any problems.

Thanks for your swift reactions, René Samson

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I am not expert in PDE, but I wonder if Mathematica can handle numerical PDEs on unbounded domains.

I would rewrite the deffinition of the function c0 with Piecewise, instead of If.